Cohomology of Categorical Self-Distributivity
By J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Masahico Saito. 2006
72 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/641aef88865676d2df6600fffeb2d69354750e55
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Homologies of Algebraic Structures via Braidings and Quantum Shuffles (2012, background): “The categorification of SD structures and of the corresponding pre-braiding is less straightforward and is done in [21] (see also [2] for an alternative construction).”