Extending Structures for Lie Conformal Algebras
Extending Structures for Lie Conformal Algebras
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DOI：
10.1007/s10468-016-9638-z
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发表时间：
2017-02
影响因子：
0.6
通讯作者：
Yanyong Hong;Yu-cai Su
中科院分区：
文献类型：
--
作者：
Yanyong Hong;Yu-cai Su
研究了李共形代数的-分裂扩张结构问题。本文引入了一个给定的李共形代数R与一个给定的模Q的统一积的定义。这个积包括了李共形代数的一些有趣的积，如扭曲积、交叉积和双交叉积。利用该积构造了一个上同调类型对象，为-分裂扩展结构问题提供了理论解答。利用这一一般理论，我们详细研究了交叉积和双交叉积，分别给出了-分裂扩张问题和-分裂因子分解问题的答案。
The-split extending structures problem for Lie conformal algebras is studied. In this paper, we introduce the definition of unified product of a given Lie conformal algebraRand a given-moduleQ. This product includes some other interesting products of Lie conformal algebras such as twisted product, crossed product, and bicrossed product. Using this product, a cohomological type object is constructed to provide a theoretical answer to the-split extending structures problem. Moreover, using this general theory, we investigate crossed product and bicrossed product in detail, which give the answers for the-split extension problem and the-split factorization problem respectively.