Title

Cohomology of Frobenius Algebras and the Yang-Baxter Equation

Document Type

Article

Publication Date

2008

Keywords

Cohomology, Frobenius algebra, Yang-Baxter equation

Digital Object Identifier (DOI)

https://doi.org/10.1142/S0219199708003022

Abstract

A cohomology theory for multiplications and comultiplications of Frobenius algebras is developed in low dimensions, in analogy with Hochschild cohomology of bialgebras, based on deformation theory. Concrete computations are provided for key examples. Skein theoretic constructions give rise to solutions to the Yang-Baxter equation, using multiplications and comultiplications of Frobenius algebras, and 2-cocycles are used to obtain deformations of R-matrices thus obtained.

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

Communications in Contemporary Mathematics, v. 10, issue supp01, p. 791-814

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