A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation

For a set theoretical solution of the Yang-Baxter equation (X, σ), we define a d.g. bialgebra B=B(X, σ), containing the semigroup algebra A=k(X)/〈xy=zt:σ(x, y)=(z, t)〉, such that k⊗AB⊗Ak and HomA-A(B, k) are respectively the homology and cohomology complexes computing biquandle homology and cohomolo...

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Autor principal: Farinati, Marco Andres
Publicado: 2016
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v220_n10_p3454_Farinati
http://hdl.handle.net/20.500.12110/paper_00224049_v220_n10_p3454_Farinati
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00224049_v220_n10_p3454_Farinati2023-06-08T14:50:43Z A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation Farinati, Marco Andres For a set theoretical solution of the Yang-Baxter equation (X, σ), we define a d.g. bialgebra B=B(X, σ), containing the semigroup algebra A=k(X)/〈xy=zt:σ(x, y)=(z, t)〉, such that k⊗AB⊗Ak and HomA-A(B, k) are respectively the homology and cohomology complexes computing biquandle homology and cohomology defined in [2,5] and other generalizations of cohomology of rack-quandle case (for example defined in [4]). This algebraic structure allows us to show the existence of an associative product in the cohomology of biquandles, and a comparison map with Hochschild (co)homology of the algebra A. © 2016 Elsevier B.V. Fil:Farinati, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v220_n10_p3454_Farinati http://hdl.handle.net/20.500.12110/paper_00224049_v220_n10_p3454_Farinati
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description For a set theoretical solution of the Yang-Baxter equation (X, σ), we define a d.g. bialgebra B=B(X, σ), containing the semigroup algebra A=k(X)/〈xy=zt:σ(x, y)=(z, t)〉, such that k⊗AB⊗Ak and HomA-A(B, k) are respectively the homology and cohomology complexes computing biquandle homology and cohomology defined in [2,5] and other generalizations of cohomology of rack-quandle case (for example defined in [4]). This algebraic structure allows us to show the existence of an associative product in the cohomology of biquandles, and a comparison map with Hochschild (co)homology of the algebra A. © 2016 Elsevier B.V.
author Farinati, Marco Andres
spellingShingle Farinati, Marco Andres
A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation
author_facet Farinati, Marco Andres
author_sort Farinati, Marco Andres
title A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation
title_short A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation
title_full A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation
title_fullStr A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation
title_full_unstemmed A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation
title_sort differential bialgebra associated to a set theoretical solution of the yang-baxter equation
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v220_n10_p3454_Farinati
http://hdl.handle.net/20.500.12110/paper_00224049_v220_n10_p3454_Farinati
work_keys_str_mv AT farinatimarcoandres adifferentialbialgebraassociatedtoasettheoreticalsolutionoftheyangbaxterequation
AT farinatimarcoandres differentialbialgebraassociatedtoasettheoreticalsolutionoftheyangbaxterequation
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