结合代数非交换扩张的微分分次李代数方法
A differential graded Lie algebra approach to non abelian extensions of associative algebras
摘要：
本文证明了结合代数$\mathcal{B}$通过结合代数$\mathcal{A}$的非交换扩张可以看作是适当的微分分次李代数$L$的Maurer-Cartan元.特别地，我们证明了$\mathcal{MC}(L)$（$L$的Deligne广群）与非交换上同调$H^2_{nab}(\mathcal{B},\mathcal{A})$是1-1对应的.
英文摘要：
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 $H^2_{nab}(\mathcal{B},\mathcal{A})$.
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