Claus Michael Ringel

Publications since 1989

Some corrections

For some of the manuscripts, dvi-files, ps-files or pdf-files are available.

Preprints

Accepted for publication

[162] Cluster-additive functions on stable translation quivers (May 8, 2011, revised Sep 22, 2011)
To appear in Journal of Algebraic Combinatorics.
[161] Minimal infinite cogeneration-closed subcategories. (Sept. 4, 2010, revised Dec 22, 2011).
To appear in Bull. Sci. math.
[160] Morphisms determined by objects: The case of modules over artin algebras (31.10.2011, revised 20.12.2012)
To appear in Illinois Journal of Mathematics.
[158] On the representation dimension of artin algebras (July 9, 2011, corrected Sept 12, 2011))
To appear in: Proceedings of the Taipei Conference on Representation Theory held in Taipei in 2010.
Bulletin of the Institute of Mathematics, Academia Sinica.
[157] Indecomposable representations of the Kronecker quivers (Sept. 29, 2010, revised version June 3, 2011).
To appear in Proceedings AMS.
[127] Hereditary triangulated categories.
Compositio Mathematica (To appear).
SFB-Preprint 98-107

2012

[159] Fahr-Ringel: Categorification of the Fibonacci Numbers Using Representations of Quivers (slightly revised, Sept 21, 2011).
Journal of Integer Sequences. Vol. 15 (2012), Article 12.2.1 Reprint

2011

[156] The minimal representation-infinite algebras which are special biserial (updated version, March 8, 2011)
In: Representations of Algebras and Related Topics,
EMS Series of Congress Reports, European Math. Soc. Publ. House, Zürich, 2011
(Editors Andrzej Skowronski and Kunio Yamagata), p.501-560.
[155] Indecomposables live in all smaller lengths
(October 10, 2009, revised August 18, 2010)
Bull. London Math. Soc. (2011) 43(4): 655-660,   doi: 10.1112/blms/bdq128
Reprint
[154] The SL3-module T(43) for p=3 (July 2, 2009). An appendix to the paper: Decomposition of tensor products of modular irreducible representations for SL3 by S.R.Doty and S.Martin arXiv, new version by Bowman, Doty, Martin (July 12, 2010)
International Electronic Journal of Algebra 9 (2011), 177-219
Final version
[153] Cluster-concealed algebras (Nov. 21, 2009)
Advances in Mathematics. 226, (2011), Pages 1513-1537

2010

[152] Gabriel-Roiter inclusions and Auslander-Reiten theory (Nov 1, 2009, slightly revised Aug 20, 2010).
Journal of Algebra 324 (2010) 3579-3590
[151] Iyama's finiteness theorem via strongly quasi-hereditary algebras (September 29, 2009)
Journal of Pure and Applied Algebra 214 (2010) 1687-1692. article
Correction: On page 4, line 4: replace Hom(u,-) by Hom(-,u).

2009

[147] The relevance and the ubiquity of Prüfer modules.
Proceedings of the 4th International Conference on Representation Theory (edt: Zongzhu Lin, Jianpan Wang). Contemporary Mathematics. Amer. Math. Soc. 478 (2009), 163-176 ISBN-10: 0-8218-4555-1, ISBN-13: 978-0-8218-4555-4
pdf

2008

[150] The first Brauer-Thrall conjecture.
In: Models, Modules and Abelian Groups. In Memory of A. L. S. Corner. Walter de Gruyter, Berlin (edt: B. Goldsmith, R.Göbel) (2008), 369-374.
pdf
[149] (with V.Dlab): The global dimension of the endomorphism ring of a generator-cogenerator for a hereditary artin algebra.
Mathematical Reports of the Academy of Science of the Royal Society of Canada. Vol 30 (2008), Nr.3, 89-96.
pdf, Published version: pdf
[148] The self-injective cluster tilted algebras.
Archiv der Mathematik. Band 91 (2008) Nr.3, 218-225.
pdf. (14.05.2008)
[146] (with M. Schmidmeier) Invariant subspaces of nilpotent operators. I.
Journal Reine Angew. Math. Band 2008, Nr. 614 (2008), 1--52.
Preprint or ArXiv math.RT/0608666
[145] (with M. Schmidmeier) The Auslander-Reiten Translation in Submodule Categories.
Trans. Amer. Math. Soc. 360 (2008), 691-716.
pdf-file.
[144] (with Ph. Fahr): A partition formula for Fibonacci numbers.
Journal of Integer Sequences, Vol. 11 (2008), Article 08.1.4. Journal of Integer Sequences, Vol. 11 (2008), Article 08.1.4.
pdf
Correction: Page 1, line -10: replace "the preprojective" by "preprojective" - one gets in this way only one τ-orbit of the preprojectives, not all!

2007

[143] The ladder construction of Prüfer modules.
Revista de la Union Matematica Argentina. (2007) Vol 48-2, p.47-65. volume 48
pdf
[142] Some remarks concerning tilting modules and tilted algebras.
Origin. Relevance. Future.
(An appendix to the Handbook of Tilting Theory.)
(ed Angeleri Hügel, Happel, Krause), London Math. Soc. Lecture Note Series vol 332. Cambridge University Press (2007). ISBN-13: 9780521680455, p.413-472.
pdf-file (Final version, May 2006)
Remark

2006

[141] The theorem of Bo Chen and Hall polynomials.
Nagoya Journal vol 183 (2006), 143-160.
pdf-file
[140] Algebras, Rings And Their Representations:
Proceedings Of The International Conference on Algebras, Modules and Rings, Lisbon, Portugal, 14-18 July 2003 (ed Facchini, Fuller, Ringel, Santa-Clara).
World Scientific Publishing Company (2006), 371 pages.
ISBN-10: 9812565981
[139] Foundation of the Representation Theory of Artin Algebras, Using the Gabriel-Roiter Measure.
In: Trends in Representation Theory of Algebras and Related Topics. (Workshop Queretaro, Mexico, 2004). Edited by de la Pena and Bautista. Contemporary Math. 406. Amer.Math.Soc. (2006), 105-135.
(Including a remark that one should be concerned about the military involvement of the publisher of the volume, the American Mathematical Society).
pdf-file. (22.04.2006)
(This version combines my Hirosaki-notes 2003, notes for the Hangzhou lectures 2005 and some additional considerations.)

[138] (with M. Schmidmeier) Submodule categories of wild representation type.
Journal for Pure and Applied Algebra 205, Issue 2, May 2006, Pages 412-422.
dvi-file, as ps-file, as pdf-file.
math.RT/0409417
[137] (with I. Reiten) Infinite dimensional representations of canonical algebras.
Canadian Journal of Mathematics 58 (2006), 180-224.
dvi-file with an Appendix: Cotorsion pairs: dvi-file, as ps-file, as pdf-file,

2005

[136] The Gabriel-Roiter measure.
Bull. Sci. math. 129 (2005), 726-748.
dvi-file, as ps-file. as pdf-file
[135] Bautista and the Development of the Representation Theory of Artin Algebras
Proceedings XV Latinamerican Colloquium of Algebra.
Contemporary Mathematics 376. Amer.Math.Soc.(2005), 89-103.
dvi-file, as pdf-file.

2004

[134] Free submodules of indecomposable modules.
dvi-file, as ps-file.
Archiv der Mathematik. 83 (2004), 17-22.
[133] Algebraically Compact Modules Arising from Tubular Families. A Survey.
(First part of a lecture presented at the International Conference on Algebra held at Suzhou (China) in 2002.)
pdf-file
Algebra Colloquium 11 (2004), 155-172.
[132] Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry.
(edited with V.Dlab)
Fields Institute Communications vol.40. Amer.Math.Soc.(2004), 1-479.

2003

[131] Special Issue: Linear Algebra Methods in Representation Theory.
(edited with J.Drozd, D.Happel).
Linear Algebra and Aplications. Volume 365 (2003), 1-467.

2002

[130] The Diamond Category of a Locally Discrete Ordered Set
In: Representations of Algebras. Vol. II (ed. D.Happel, Y.B.Zhang). BNU Press. 387-395.
File: pdf-file and
[129] A Ray Quiver Construction of Hereditary Abelian Categories with Serre Duality
In: Representations of Algebras. Vol. II (ed. D.Happel, Y.B.Zhang). BNU Press. 396-416.
File: dvi-file and ps-file
[128] Combinatorial Representation Theory: History and Future.
In: Representations of Algebras. Vol. I (ed. D.Happel, Y.B.Zhang). BNU Press. 122-144.
File: dvi-file and ps-file pdf-file

2001

[124] Algebra at the turn of the century.
Southeast Asian Bulletin of Mathematics 25 (2001), 147-160. DVI-File pdf-File

(Chinese Translation) in: Algebra in the 21. Century. Beijing (2002), 16-32.
Springer-Link
[125] Krull-Remak Schmidt fails for artinian modules over local rings.
Algebras and Representation Theory 4 (2001), 77-86. SFB-Preprint 99-110
[126] On generic modules for string algebras.
Bol. Soc. Mat. Mexicana (3) 7 (2001), 85-97. SFB-Preprint 99-045, pdf-file

2000

[121] (ed. with H. Krause) Infinite Length Modules.
Trends in Mathematics. Birkhäuser Verlag.
Birkhäuser Verlag (2000), ISBN 3-7643-6413-0
[122] Infinite length modules. Some examples as introduction.
In: Infinite length modules. Trends in Mathematics. Birkhäuser Verlag [121], 1-73. DVI-File, pdf
[123] The representation type of the full transformation semigroups.
Semigroup Forum 61 (2000), 429-434. SFB-Preprint 99-078

1999

[117] (with Th. Brüstle, L. Hille, G. Röhrle): The Delta-filtered modules without self-extensions for the Auslander algebra of k[T]/ < Tn > .
Algebras and Representation Theory. 2 (1999), 295-312 SFB-Preprint 98-067
[118] (ed. with P.Dräxler, G.O.Michler) Computational Methods for Representations of Groups and Algebras.
Progress in Mathematics. 1999 (357+14 pages). ISBN 3-7643-6063-1, ISBN 0-8176-6063-1.
[119] Tame algebras are Wild
Algebra Colloquium 6 (1999), 473-480. SFB-Preprint 99-044
[120] The multisegment duality and the preprojective algebras of type A.
Algebra Montpellier Announcements. 1.1 (1999) (6 pages). SFB-Preprint 99-108

1998

[112] Exceptional modules are tree modules.
Lin. Alg. Appl. 275-276 (1998) 471-493. SFB-Preprint 96-082.
[113] The Ziegler spectrum of a tame hereditary algebra.
Coll. Math. 76 (1998), 105-115. SFB-Preprint 97-035.
[114] The preprojective algebra of a quiver.
In: Algebras and Modules II. Can. Math. Soc. Conference Proceedings. Vol. 24 (1998), 467-480. SFB-Preprint 97-046.
[115] (with I. Ágoston and E. Lukács) Realization of Frobenius functions.
J. Algebra 210 (1998), 419-439. SFB-Preprint 97-096.
[116] The preprojective algebra of a tame quiver: The irreducible components of the module varieties.
In: Trends in the Representation Theory of Finite Dimensional Algebras (ed. E.Green, B. Huisgen-Zimmermann). Contemporary Math. 229. Providence, RI, 1998, 293-306
(partly in: SFB-Preprint 97-046).

1997

[108] Quantum Serre relations.
Proc. Reims Conference. Séminaire et Congrês 2, Soc. Math. France. (1997) 137-148. SFB-Preprint 95-083 (1995)
[109] The development of the representation theory of finite dimensional algebras. 1968 - 1975.
In: Representation Theory and Algebraic Geometry. Ed. A. Martsinkovsky, G. Todorov. London Math. Soc. Lecture Note Series 238. Cambridge University Press, Cambridge 1997, p.89-115. ISBN 0-521-57789-6
[110] A construction of endofinite modules.
Advances in Algebra and Model Theory. Gordon-Breach. (ed. M. Droste, R. Göbel). London (1997) p. 387-399 SFB Preprint 96-033.
[111] The repetitive algebra of a gentle algebra.
Bol. Soc. Mat. Mexicana (3). Vol 3 (1997), 235-253. SFB-Preprint 97-024.

1996

[101] PBW-bases of quantum groups.
Journal Reine Angew. Math. 470 (1996), 51-88.
[102] (with I. Ágoston and E. Lukács) Frobenius functions on translation quivers.
In: Representation Theory of Algebras. CMS Conference Proceedings 18. Providence (1996), 17-37.
[103] Cones.
In: Representation Theory of Algebras. CMS Conference Proceedings 18. Providence (1996), 583-586.
[104] The Liu-Schulz example.
In: Representation Theory of Algebras. CMS Conference Proceedings 18. Providence (1996), 587-600.
[105] Maurice Auslander and the representation theory of artin algebras.
In: Representation Theory of Algebras. CMS Conference Proceedings 18. Providence (1996), 4-12.
[106] Green's Theorem on Hall algebras.
In: Representation Theory of Algebras and Related Topics. CMS Conference Proceedings 19. Providence (1996), 185-245.
dvi-file, ps-file, pdf-file.
Corrections
[107] Exceptional objects in hereditary categories.
Proceedings Constantza Conference. An. St. Univ. Ovidius Constantza Vol. 4 (1996), f. 2, 150-158.
pdf-file.

1995

[99] Some algebraically compact modules I.
In: Abelian Groups and Modules (ed. A. Facchini and C. Menini). Kluwer (1995), 419-439.
[100] The Hall algebra approach to quantum groups. Proceedings
E.L.A.M., Mexico, D.F. and Guanajuato 1993. Aportaciones Matemáticas Comunicaciones 15 (1995), 85-114.
This is the written version of the E.L.A.M. Lectures 1993;
dvi-file, ps-file, pdf-file.

1994

[97] The spectral radius of the Coxeter transformations for a generalized Cartan matrix.
Math.Annalen 300 (1994), 331-339.
[98] The braid group action on the set of exceptional sequences of a hereditary algebra.
In: Abelian Group Theory and Related Topics. Contemp. Math. 171 (1994), 339-352.

1993

[94] The composition algebra of a cyclic quiver. Towards an explicit description of the quantum group of type $\tilde A_n.$
Proceedings London Math. Soc. (3) 66 (1993), 507-537.
[95] Hall algebras revisited.
Israel Mathematica Conference Proceedings. Vol.7 (1993), 171-176.
dvi-file, ps-file, pdf-file.
[96] (mit D. Happel) Directing projective modules.
Archiv der Math. 60 (1993), 237-246.

1992

[86] From representations of quivers via Hall and Loewy algebras to quantum groups.
Proceedings Novosibirsk Conference 1989. Contemporary Mathematics 131 (Part 2) (1992), 381-401
dvi-file, ps-file, pdf-file.
[87] The category of good modules over a quasi-hereditary algebra.
Accepted for publication by the editors of the Proceedings of the Tsububa International Conference 1990 (CMS Conference Proc. Vol 11, 199), but the publisher of the Proceddings, the American Mathematical Society, has refused to print the paper, since it contains the following remark:
This paper is written in English in order to be accessible to readers through-out the world, but we would like to stress that this does not mean that we support any imperialism. Indeed, we were shocked when we heard that the Iraki military machinery was going to bomb Washington in reaction to the US invasion in Grenada and Panama, but maybe we were misinformed by the nowadays even openly admitted censorship.
(The copyright of the paper is still with the American Mathematical Society.)
(Preprint: Carleton-Ottawa Lect. Note Ser. 14, Exp. 30, 1992).
[88] On contravariantly finite subcategories.
Accepted for publication by the editors of the Proceedings of the Tsububa International Conference 1990 (CMS Conference Proc. Vol 11, 199), but the publisher of the Proceddings, the American Mathematical Society, has refused to print the paper, since it contains the following remark:
This paper is written in English in order to be accessible to readers through-out the world, but we would like to stress that this does not mean that we support any imperialism. Indeed, we were shocked when we heard that the Iraki military machinery was going to bomb Washington in reaction to the US invasion in Grenada and Panama, but maybe we were misinformed by the nowadays even openly admitted censorship.
(The copyright of the paper is still with the American Mathematical Society.)
(Preprint: Carleton-Ottawa Lect. Note Ser. 14, Exp. 29, 1992).
[89] (mit V. Dlab) The module theoretical approach to quasi-hereditary algebras.
In: Representations of Algebras and Related Topics (ed. H. Tachikawa and S. Brenner). London Math. Soc. Lecture Note Series 168. Cambridge University Press (1992), 200-224
pdf-File (of an early ms)
[90] Lie algebras (arising in representation theory).
In: Representations of Algebras and Related Topics (ed. H. Tachikawa and S. Brenner). London Math. Soc. Lecture Note Series 168. Cambridge University Press (1992), 284-291.
pdf
[91] (mit W. Crawley-Boevey und D. Happel) A bypass of an arrow is sectional.
Archiv der Math. 58 (1992), 525-528.
[92] The use of the representation theory of finite-dimensional hereditary algebras.
In: Proceedings First China-Japan International Symposium on Ring Theory. Okayama (1992), 121-126.
[93] (mit W. Crawley-Boevey) Algebras whose Auslander-Reiten quivers have large regular components.
J. Algebra 153 (1992), 494-516.

1991

[83] (mit V. Dlab) Towers of semi-simple algebras.
J. Funct. Analysis 102 (1991), 35-46
[84] The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences.
Math. Z. 208 (1991), 209-223.
[85] Recent advances in the representation theory of finite dimensional algebras.
In: Progress in Math. 95 (1991), 141-192.

1990

[77] (mit V. Dlab) The dimension of a quasi-hereditary algebra.
In: Topics in Algebra. Banach Center Publ. 26. (1990).
[78] (mit V. Dlab) The Hochschild cocycle corresponding to a long exact sequence.
Tsukuba J. Math. 14 (1990), 489-496.
[79] The canonical algebras. (With an appendix by W. Crawley-Boevey).
In: Topics in Algebra. Banach Center Publ. 26. (1990), 407-432.
[80] Hall algebras.
In: Topics in Algebra. Banach Center Publ. 26. (1990), 433-447.
[81] Hall polynomials for the representation-finite hereditary algebras.
Adv. Math. 84 (1990), 137-178
[82] Hall algebras and quantum groups.
Inventiones math. 101 (1990), 583-592.

1989

[76] (mit V. Dlab) Filtrations of right ideals related to projectivity of left ideals.
In: Sem. Malliavin. Springer LNM. 1404 (1989), 95-107.
[75] (mit V. Dlab) A construction for quasi-hereditary algebras.
Compositio Math. 70 (1989), 155-175.
[74] (mit V. Dlab) Every semiprimary ring is the endomorphism ring of a projective module over a quasi-hereditary ring.
Proc. Amer. Math. Soc. 107 (1989), 1-5.
[73] (mit V. Dlab) Auslander algebras as quasi-hereditary algebras.
J. London Math. Soc. 39 (1989), 457-466.
[72] (mit V. Dlab) Quasi-hereditary algebras.
Illinois J. 33 (1989), 280-291.
[71] (mit V. Dlab) On modular representations of $A_4$.
J. Algebra 123 (1989), 506-522.

Some Reviews

On: G. Lusztig: Introduction to Quantum Groups.
Zeitschrift für Analysis und ihre Anwendungen 13 (1994), 756-760.
On: P. Gabriel, A.V.Roiter: Representations of Finite-dimensional Algebras. (Encyclopaedia of Mathematical Sciences, vol. 73. Kostrikin, Shafarevich (ed.): Algebra VIII)
Jahresberichte der DMV, vol.98 (1996), p.29-34
On: M. Auslander, I. Reiten, S.O. Smalø: Representation Theory of Artin algebras.
Bulletin Amer. Math. Soc. 33, Number 4, October 1996.
On: G. Lusztig: Quiver Varieties.
Featured Review. Math. Reviews.
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Fakultät für Mathematik, Universität Bielefeld
Verantwortlich: C.M.Ringel
E-Mail: ringel@mathematik.uni-bielefeld.de
May 12, 2000