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...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00224049_v220_n10_p3454_Farinati |
| Aporte de: |
| Sumario: | 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. |
|---|