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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
