论文标题
交叉模块，联想保形代数的非亚伯扩展和井序
Crossed modules, non-abelian extensions of associative conformal algebras and Wells exact sequences
论文作者
论文摘要
在本文中，我们介绍了缔合形式代数的交叉模块，两项强烈同型联想保形代数，并讨论了它们与联想共同代数的第3--霍奇斯柴尔德共同体之间的关系。我们通过引入非亚伯式的共同体来对非亚洲扩展进行分类。我们表明，可以将关联保形代数的非亚伯扩展视为合适的差异分级Lie代数的Maurer-Cartan元素，并证明这种差异分级的Deligne lie代数的Deligne Groupoid与非阿布尔同胞相对应。基于此分类，我们研究了一对自动形态的诱导性，这些自动形态关于联想保串代数的非 - 亚伯延伸，并在关联保形代数的背景下给出了井的基本序列。最后，我们考虑了一对衍生物的扩展性，涉及关联保形代数的阿贝尔扩展，并提供精确的井类型序列。
In this paper, we introduce the notions of crossed module of associative conformal algebras, 2-term strongly homotopy associative conformal algebras, and discuss the relationship between them and the 3-th Hochschild cohomology of associative conformal algebras. We classify the non-abelian extensions by introducing the non-abelian cohomology. We show that non-abelian extensions of an associative conformal algebra can be viewed as Maurer-Cartan elements of a suitable differential graded Lie algebra, and prove that the Deligne groupoid of this differential graded Lie algebra corresponds one to one with the non-abelian cohomology. Based on this classification, we study the inducibility of a pair of automorphisms about a non-abelian extension of associative conformal algebras, and give the fundamental sequence of Wells in the context of associative conformal algebras. Finally, we consider the extensibility of a pair of derivations about an abelian extension of associative conformal algebras, and give an exact sequence of Wells type.
