The Moore Complex of a Simplicial Cocommutative Hopf Algebra
Kadir Emir
TL;DR
This paper develops a new framework for understanding the Moore complex of simplicial cocommutative Hopf algebras, leading to a unified theory of 2-crossed modules that bridges group and Lie algebra theories.
Contribution
It introduces a coherent definition of 2-crossed modules of cocommutative Hopf algebras, unifying existing theories for groups and Lie algebras.
Findings
Defined 2-crossed modules of cocommutative Hopf algebras.
Unified the 2-crossed module theories of groups and Lie algebras.
Provided a new perspective on the structure of simplicial cocommutative Hopf algebras.
Abstract
We study the Moore complex of a simplicial cocommutative Hopf algebra through Hopf kernels. The most striking result to emerge from this construction is the coherent definition of 2-crossed modules of cocommutative Hopf algebras. This unifies the 2-crossed module theory of groups and of Lie algebras when we take the group-like and primitive functors into consideration.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology