Cohomology of Frobenius Algebras and the Yang-Baxter Equation

Authors

J. Scott Carter, University of South Alabama
Alissa S. Crans, Loyola Marymount UniversityFollow
Mohamed Elhamdadi, University of South Florida
Enver Karadayi, University of South Florida
Masahico Saito, University of South Florida

Document Type

Article - post-print

Publication Date

2013

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.

Comments

This article is the post-print version.

Original Publication Citation

Carter, J.S.; Crans, A.; Elhamdadi, M.; Karadayi, E.; and Saito, M. “Cohomology of Frobenius Algebras and the Yang-Baxter Equation.” Communications in Contemporary Mathematics, Vol. 10 (2008), No. 1 supp: 791 – 814.

Digital Commons @ LMU & LLS Citation

Scott Carter, J.; Crans, Alissa S.; Elhamdadi, Mohamed; Karadayi, Enver; and Saito, Masahico, "Cohomology of Frobenius Algebras and the Yang-Baxter Equation" (2013). Mathematics, Statistics and Data Science Faculty Works. 68.
https://digitalcommons.lmu.edu/math_fac/68