论文标题
平均代数，$ l_ \ iftty $ - 结构和同型平均代数代数的共同体理论
Cohomology theory of averaging algebras, $L_\infty$-structures and homotopy averaging algebras
论文作者
论文摘要
本文研究了代数的平均代数，该代数赋予了平均操作员。我们开发了一种平均代数的共同论理论，并通过将较低程度的同胞组解释为正式的变形和平均代数的阿贝尔扩展来证明其合理性。我们将$ l_ \ infty $ - 代数结构定义为定义共同体学组的$ l_ \ infty $ - 代数结构，并介绍了同型平均代数为Maurer-cartan元素的概念。
This paper studies averaging algebras, say, associative algebras endowed with averaging operators. We develop a cohomology theory for averaging algebras and justify it by interpreting lower degree cohomology groups as formal deformations and abelian extensions of averaging algebras. We make explicit the $L_\infty$-algebra structure over the cochain complex defining cohomology groups and introduce the notion of homotopy averaging algebras as Maurer-Cartan elements of this $L_\infty$-algebra.
