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arXiv · 2404.15868

On a general notion of a polynomial identity and codimensions

A. S. Gordienko
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Abstract

Using the braided version of Lawvere's algebraic theories and Mac Lane's PROPs, we introduce polynomial identities for arbitrary algebraic structures in a braided monoidal category C as well as their codimensions in the case when C is linear over some field. The new cases include coalgebras, bialgebras, Hopf algebras, braided vector spaces, Yetter-Drinfel'd modules, etc. We find bases for polynomial identities and calculate codimensions in some important particular cases.

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A. S. Gordienko. 2024-04-24. On a general notion of a polynomial identity and codimensions. https://doi.org/10.1016/j.jpaa.2024.107814

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