%0 Generic %1 Carter2006a %A Carter, J. Scott %A Crans, Alissa %A Elhamdadi, Mohamed %A Saito, Masahico %D 2006 %K algebra category-theory homology quandles %T Cohomology of Categorical Self-Distributivity %U http://arxiv.org/abs/math/0607417 %X We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The self-distributive operations of these structures provide solutions of the Yang--Baxter equation, and, conversely, solutions of the Yang--Baxter equation can be used to construct self-distributive operations in certain categories. Moreover, we present a cohomology theory that encompasses both Lie algebra and quandle cohomologies, is analogous to Hochschild cohomology, and can be used to study deformations of these self-distributive structures. All of the work here is informed via diagrammatic computations.

@misc{Carter2006a, abstract = { We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The self-distributive operations of these structures provide solutions of the Yang--Baxter equation, and, conversely, solutions of the Yang--Baxter equation can be used to construct self-distributive operations in certain categories. Moreover, we present a cohomology theory that encompasses both Lie algebra and quandle cohomologies, is analogous to Hochschild cohomology, and can be used to study deformations of these self-distributive structures. All of the work here is informed via diagrammatic computations. }, added-at = {2009-05-22T15:47:16.000+0200}, author = {Carter, J. Scott and Crans, Alissa and Elhamdadi, Mohamed and Saito, Masahico}, biburl = {https://www.bibsonomy.org/bibtex/23705a6a6cb367887fbeb504496def4e8/njj}, description = {Cohomology of Categorical Self-Distributivity}, interhash = {0277b09b489e58cbf11dacbc09c1d218}, intrahash = {3705a6a6cb367887fbeb504496def4e8}, keywords = {algebra category-theory homology quandles}, note = {cite arxiv:math/0607417 Comment: 48 pages, 43 figures, uses diagram.sty, some proofs appear in appendix Some typos corrected, minor clarification of statements and notation}, timestamp = {2009-05-22T15:47:16.000+0200}, title = {Cohomology of Categorical Self-Distributivity}, url = {http://arxiv.org/abs/math/0607417}, year = 2006 }