A differential graded Lie algebra approach to non abelian extensions of associative algebras
Abstract
In this paper we show that non abelian extensions of an associative algebra $\mathcal{B}$ by an associative algebra $\mathcal{A}$ can be viewed as Maurer-Cartan elements of a suitable differential graded Lie algebra $L$. In particular we show that $\mathcal{MC}(L)$, the Deligne groupoid of $L$, is in 1-1 correspondence with the non-abelian cohomology $H^2_{nab}(\mathcal{B},\mathcal{A})$.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2018
- DOI:
- 10.48550/arXiv.1802.04641
- arXiv:
- arXiv:1802.04641
- Bibcode:
- 2018arXiv180204641G
- Keywords:
-
- Mathematics - Algebraic Topology;
- Mathematics - Quantum Algebra;
- 18G50;
- 20J06