Cohomology and extensions of braces
Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories. These theories mix the Harrison (co)homology for the abelian group st...
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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00308730_v284_n1_p191_Lebed |
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| Sumario: | Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories. These theories mix the Harrison (co)homology for the abelian group structure and the (co)homology theory for general cycle sets, developed earlier by the authors. Different classes of brace extensions are completely classified in terms of second cohomology groups. © 2016 Mathematical Sciences Publishers. |
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