Unique Tensor Factorization of Algebras

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1998
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Nüsken, Michael
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Zusammenfassung

Tensor product decomposition of algebras is known to be non-unique in many cases. But, as will be shown here, an additively indecomposable, finite-dimensional C-algebra A has an essentially unique tensor factorization A=A1x...xAr into non-trivial, x-indecomposable factors Ai. Thus the semiring of isomorphism classes of finite-dimensional C-algebras is a polynomial semiring N[X]. Moreover, the field C of complex numbers can be replaced by an arbitrary field of characteristic zero if one restricts oneself to SCHURian algebras.

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ISO 690NÜSKEN, Michael, 1998. Unique Tensor Factorization of Algebras
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@techreport{Nusken1998Uniqu-6356,
  year={1998},
  series={Konstanzer Schriften in Mathematik und Informatik},
  title={Unique Tensor Factorization of Algebras},
  number={76},
  author={Nüsken, Michael}
}
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