Cohomology of Frobenius Algebras and the Yang-Baxter Equation
Cohomology, Frobenius algebra, Yang-Baxter equation
Digital Object Identifier (DOI)
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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Citation / Publisher Attribution
Communications in Contemporary Mathematics, v. 10, issue supp01, p. 791-814
Scholar Commons Citation
Carter, J. Scott; Crans, Alissa S.; Elhamdadi, Mohamed; Karadayi, Enver; and Saito, Masahico, "Cohomology of Frobenius Algebras and the Yang-Baxter Equation" (2008). Mathematics and Statistics Faculty Publications. 127.