Crossed modules and cohomology of algebras over an operad
Abstract
We introduce a general definition of an n-crossed module of P-algebras over an algebraic operad P, which coincides with historical definitions in the cases of the operads A s or Li e and n D 1.Over a field of characteristic 0, we establish a natural isomorphism between the abelian group of equivalence classes of n-crossed modules over a pair .A; M / for an operad P and the .nC1/-stoperadic cohomology group of A with coefficients in M .
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Advanced Operator Algebra Research
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 7
- Pages
- 2635–2658
- Publication date
- 1 September 2026
- Language
- EN