Cohomology of frobenius algebras and the Yang-Baxter equation

J. Scott Carter; Alissa S. Crans; Mohamed Elhamdadi; Enver Karadayi; Masahico Saito

doi:10.1142/S0219199708003022

Cohomology of frobenius algebras and the Yang-Baxter equation

J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Enver Karadayi, Masahico Saito

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	791-814
Number of pages	24
Journal	Communications in Contemporary Mathematics
Volume	10
Issue number	1
DOIs	https://doi.org/10.1142/S0219199708003022
State	Published - Jan 16 2013

ASJC Scopus Subject Areas

General Mathematics
Applied Mathematics

Keywords

Cohomology
Frobenius algebra
Yang-Baxter equation

Disciplines

Algebra

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10.1142/S0219199708003022

https://digitalcommons.lmu.edu/math_fac/68

Cite this

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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.",

keywords = "Cohomology, Frobenius algebra, Yang-Baxter equation",

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AU - Saito, Masahico

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N2 - 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.

AB - 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.

KW - Cohomology

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KW - Yang-Baxter equation

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Cohomology of frobenius algebras and the Yang-Baxter equation

Abstract

ASJC Scopus Subject Areas

Keywords

Disciplines

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