On the Dimension of a Composition Algebra

by Markus Rost (Markus Rost, 5 pages)

The possible dimensions of a composition algebra are 1, 2, 4, or 8. We give a tensor categorical argument.

Documenta Mathematica, Vol. 1 (1996), 209-214


Ein tensorkategorieller Zugang zum Satz von Hurwitz

by Dominik Boos (Diplomarbeit ETH Zürich, March 1998, 42 pages)

The thesis describes the graphical technique mentioned in the article [M. Rost, On the Dimension of a Composition Algebra, Doc. Math. 1 (1996), 209-214].

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Vektorproduktalgebren

by Susanne Maurer (Diplomarbeit Universität Regensburg, April 1998, 39 pages)

The thesis describes an alternative tensor categorial argument for the possible dimensions of a composition algebra, different from the one in [M. Rost, On the Dimension of a Composition Algebra, Doc. Math. 1 (1996), 209-214].

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On Vector Product Algebras

by Markus Rost (1996, compiled in July 2004, 9 pages)

This text contains some remarks on vector product algebras and the graphical techniques. It is partially contained in the diploma thesis of D. Boos and S. Maurer.

Full text (version of July 12, 2004): [ps] [ps.gz] [pdf] [pdf.gz]


Graphical description of an axiom for vector products


On the dimension and other numerical invariants of algebras and vector products

by Larissa Cadorin, Max-Albert Knus and Markus Rost (32 pages)

Algebra and Number Theory: Proceedings of the Silver Jubilee Conference University of Hyderabad/edited by Rajat Tandon. New Delhi, Hindustan Book Agency, 2005, xii, 399 p., ISBN 81-85931-57-7

MR 2193344, Zbl 1107.17001.

Tensor categorical and diagrammatic techniques can be used to compute the dimension and other numerical invariants for algebras defined by tensor identities. These techniques are described and applied to symmetric compositions and 3-vector products.

Full text (version of April 7, 2005): [pdf] [ps] [ps.gz]


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