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Mathematics > Rings and Algebras

Title: On a general notion of a polynomial identity and codimensions

Authors: A.S. Gordienko
(Submitted on 24 Apr 2024 (v1), last revised 7 May 2024 (this version, v2))
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.
Comments: 26 pages; added a remark that in order to force a BMAT to be symmetric, it is sufficient to impose a single polynomial identity $\tau_{1,1}^2\equiv \id_2$
Subjects: Rings and Algebras (math.RA); Category Theory (math.CT); Quantum Algebra (math.QA); Representation Theory (math.RT)
MSC classes: Primary 16R10, Secondary 08B20, 16R50, 16T05, 16T15, 17A01, 18C10, 18M15
Cite as: arXiv:2404.15868 [math.RA]
  (or arXiv:2404.15868v2 [math.RA] for this version)

Submission history

From: Alexey Sergeevich Gordienko [view email]
[v1] Wed, 24 Apr 2024 13:34:09 GMT (30kb)
[v2] Tue, 7 May 2024 19:31:26 GMT (30kb)
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