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Abstract:

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.

Registro:

Documento: Artículo
Título:A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation
Autor:Farinati, M.A.; García Galofre, J.
Filiación:IMAS CONICET, Dep. de Matemática, Fac. de Cs. Exactas y Naturales, UBA, Argentina
Año:2016
Volumen:220
Número:10
Página de inicio:3454
Página de fin:3475
DOI: http://dx.doi.org/10.1016/j.jpaa.2016.04.010
Título revista:Journal of Pure and Applied Algebra
Título revista abreviado:J. Pure Appl. Algebra
ISSN:00224049
CODEN:JPAAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v220_n10_p3454_Farinati

Referencias:

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Citas:

---------- APA ----------
Farinati, M.A. & García Galofre, J. (2016) . A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation. Journal of Pure and Applied Algebra, 220(10), 3454-3475.
http://dx.doi.org/10.1016/j.jpaa.2016.04.010
---------- CHICAGO ----------
Farinati, M.A., García Galofre, J. "A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation" . Journal of Pure and Applied Algebra 220, no. 10 (2016) : 3454-3475.
http://dx.doi.org/10.1016/j.jpaa.2016.04.010
---------- MLA ----------
Farinati, M.A., García Galofre, J. "A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation" . Journal of Pure and Applied Algebra, vol. 220, no. 10, 2016, pp. 3454-3475.
http://dx.doi.org/10.1016/j.jpaa.2016.04.010
---------- VANCOUVER ----------
Farinati, M.A., García Galofre, J. A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation. J. Pure Appl. Algebra. 2016;220(10):3454-3475.
http://dx.doi.org/10.1016/j.jpaa.2016.04.010