On a general notion of a polynomial identity and codimensions

Autor:	Gordienko, A. S.
Rok vydání:	2024
Předmět:	Mathematics - Rings and Algebras Mathematics - Category Theory Mathematics - Quantum Algebra Mathematics - Representation Theory Primary 16R10 Secondary 08B20 16R50 16T05 16T15 17A01 18C10 18M15
Druh dokumentu:	Working Paper
Popis:	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. Comment: 26 pages; minor improvements
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.15868 Zobrazit plný text záznamu View this record from Arxiv