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

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].

Full text: [dvi] [dvi.gz] [ps] [ps.gz] [pdf] [pdf.gz]

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].

Full text: [dvi] [dvi.gz] [ps] [ps.gz] [pdf] [pdf.gz]

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]

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

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]

- Also available as Preprint No. 185 on Linear Algebraic Groups and Related Structures, Preprint Server, Bielefeld
- Also available as Preprint No. 191 on Jordan Theory Preprint Archives
- Listing of Hindustan Books Agency
- Promotion of Vedams eBooks