论文标题
控制$ l_ \ infty $ -Algebra，嵌入张量和Lie-Leibniz三元组的同型和同型
The controlling $L_\infty$-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples
论文作者
论文摘要
在本文中，我们首先构建了嵌入张量和Lie-leibniz三元组的控制代数，这些代数分别是分级的谎言代数和$ l_ \ infty $ -Algebra。然后，我们介绍了嵌入张量和Lie-leibniz三元组的表示和共同体，并表明连接各种共同体有一个很长的精确序列。作为应用程序，我们使用第二个共同体学组对无限变形和中央扩展进行了分类。最后，我们介绍了同型嵌入张量的概念，该张张量会引起leibniz $ _ \ infty $ -Algebra。我们意识到Kotov和Strobl的构建$ l_ \ infty $ - 代数，从嵌入张量张量，从同型嵌入张量的函数到Leibniz $ _ \ Infty $ algebras的函数，以及$ l_ \ flty $ l_ \ fly Inffty $ -Algebras的功能。
In this paper, we first construct the controlling algebras of embedding tensors and Lie-Leibniz triples, which turn out to be a graded Lie algebra and an $L_\infty$-algebra respectively. Then we introduce representations and cohomologies of embedding tensors and Lie-Leibniz triples, and show that there is a long exact sequence connecting various cohomologies. As applications, we classify infinitesimal deformations and central extensions using the second cohomology groups. Finally, we introduce the notion of a homotopy embedding tensor which will induce a Leibniz$_\infty$-algebra. We realize Kotov and Strobl's construction of an $L_\infty$-algebra from an embedding tensor, to a functor from the category of homotopy embedding tensors to that of Leibniz$_\infty$-algebras, and a functor further to that of $L_\infty$-algebras.
