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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todo:paper_00224049_v220_n10_p3454_Farinati2023-10-03T14:32:44Z A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation Farinati, M.A. García Galofre, J. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00224049_v220_n10_p3454_Farinati |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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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. |
| format |
JOUR |
| author |
Farinati, M.A. García Galofre, J. |
| spellingShingle |
Farinati, M.A. García Galofre, J. A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation |
| author_facet |
Farinati, M.A. García Galofre, J. |
| author_sort |
Farinati, M.A. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00224049_v220_n10_p3454_Farinati |
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