ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16. Nüsken, Michael, University of Constance, Germany Unique Tensor Factorization of Algebras. Tensor product decomposition of algebras is known to be non-unique in general. However, an additively indecomposable, finite dimensional ℂ-alge-bra A has an essentially unique tensor factorization

A = A_{1} ⊗ … ⊗ A_{r}

into non-trivial, ⊗-indecomposable factors A_{i} (joint result with V. Strassen). Thus the semiring of isomorphism classes of finite dimensional ℂ-algebras is a polynomial semiring ℕ[X]. This can be generalized to certain classes of algebras over other fields. Reference: Nüsken, Michael (1998), Unique Tensor Factorization of Algebras. Dissertation, Universität Konstanz. UFO-Verlag, Allensbach, ISBN 3-

930803-33-X. http://www.mathe.uni-konstanz.de/~nuesken/wrt/disseration.html