Matched pairs of Lie algebroids
Matched pairs of Lie algebroids
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DOI：
10.1017/s0017089500032055
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发表时间：
1997-05
影响因子：
0.5
通讯作者：
T. Mokri
中科院分区：
文献类型：
--
作者：
T. Mokri
摘要我们将李代数胚的概念推广到李代数上，这些概念被称为双重李代数（Lu和Weinstein），匹配的李代数对（Majid），或李代数的双曲扩张（Kosmann-Schwarzbach和Magri）。证明了一对匹配李群胚诱导一对匹配李代数胚。相反，我们证明了在一定条件下，一对匹配的李代数胚集成到一对匹配的李群胚。匹配对的李代数胚的重要性最近已经证明了陆。
Abstract We extend to Lie algebroids the notion variously known as a double Lie algebra (Lu and Weinstein), matched pair of Lie algebras (Majid), or twilled extension of Lie algebras (Kosmann-Schwarzbach and Magri). It is proved that a matched pair of Lie groupoids induces a matched pair of Lie algebroids. Conversely, we show that under certain conditions a matched pair of Lie algebroids integrates to a matched pair of Lie groupoids. The importance of matched pairs of Lie algebroids has been recently demonstrated by Lu.