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Alissa Crans
Article
Cohomology of Frobenius Algebras and the Yang-Baxter Equation
Communications in Contemporary Mathematics
  • J. Scott Carter, University of South Alabama
  • Alissa S. Crans, Loyola Marymount University
  • Mohamed Elhamdadi, University of South Florida
  • Enver Karadayi, University of South Florida
  • Masahico Saito, University of South Florida
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Document Type
Article - post-print
Publication Date
1-1-2013
Disciplines
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.

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This article is the post-print version.

Citation Information
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.