Cohomology of Frobenius Algebras and the Yang-Baxter Equation

Details Cohomology of Frobenius Algebras and the Yang-Baxter Equation Cohomology of Frobenius Algebras and the Yang-Baxter Equation

2008-01-16

arxiv.org/abs/0801.2567v1

Mathematics

Quantum Algebra

21 pages, 18 figures, in memory of Xiao Song Lin

Scientific paper

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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