COHOMOLOGY OF FROBENIUS ALGEBRAS AND THE YANG-BAXTER EQUATION-Reference-Cited by-同舟云学术

COHOMOLOGY OF FROBENIUS ALGEBRAS AND THE YANG-BAXTER EQUATION

Published:2008-11 Issue:supp01 Volume:10 Page:791-814
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

CARTER J. SCOTT¹,CRANS ALISSA S.²,ELHAMDADI MOHAMED³,KARADAYI ENVER³,SAITO MASAHICO³

Affiliation:

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

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

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

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199708003022

Reference19 articles.

1. A NOTE ON THE BAR-NATAN SKEIN MODULE

2. Quandle cohomology and state-sum invariants of knotted curves and surfaces

3. Cohomology of the adjoint of Hopf algebras

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