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COHOMOLOGY OF FROBENIUS ALGEBRAS AND THE YANG-BAXTER EQUATION

J. SCOTT CARTER

Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA

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ALISSA S. CRANS

Department of Mathematics, Loyola Marymount University, Los Angeles, CA 90045, USA

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MOHAMED ELHAMDADI

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

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ENVER KARADAYI

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

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, and

MASAHICO SAITO

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

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https://doi.org/10.1142/S0219199708003022Cited by:10 (Source: Crossref)

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.

To the memory of Xiao-Song Lin

Keywords:

AMSC: 16W30, 57M25

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