3-Crossed Modules of Commutative Algebras

Abstract

In this paper we define 3-crossed modules for commutative (Lie) algebras and investigate the relation between this construction and the simplicial algebras. Also we define the projective 3-crossed resolution for investigate a higher dimensional homological information and show the existence of this resolution for an arbitrary $\mathbf{k}$-algebra.

16 pages

Cited by in corpus (2)

• From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets
• 3-form Yang-Mills based on 2-crossed modules