弗罗贝纽斯·普雷拉德就是科苏尔
The Frobenius properad is Koszul
摘要：
我们显示Koszulness的道具管理对合李双代数和道具管理非酉和酉-酉Frobenius代数，解决了一个长期存在的问题。这给了我们极小模型，其变形复合物，并为变形复合物的代数进行了详细讨论。利用图复形的操作数，借助于作者之一的一个早期结果，我们证明了Grothendieck-Teichmüller群$GRT_1$在由自同构支配的李双代数和对合李双代数的适当标的极小模型上有一个高度非平凡的作用.作为推论，我们得到了一个由Grothendieck-Teichmüller李代数的元素参数化的任何（对合）李双代数和任何Frobenius代数的一大类泛变形。我们还证明了，对于任何给定的同伦对合李双代数结构在一个向量空间中，有一个相关的同伦Batalin-Vilkovisky代数结构的相关Chevalley-Eilenberg复形。
英文摘要：
We show Koszulness of the prop governing involutive Lie bialgebras and also of the props governing non-unital and unital-counital Frobenius algebras, solving a long-standing problem. This gives us minimal models for their deformation complexes, and for deformation complexes of their algebras which are discussed in detail. Using an operad of graph complexes we prove, with the help of an earlier result of one of the authors, that there is a highly non-trivial action of the Grothendieck-Teichmüller group $GRT_1$ on (completed versions of) the minimal models of the properads governing Lie bialgebras and involutive Lie bialgebras by automorphisms. As a corollary one obtains a large class of universal deformations of any (involutive) Lie bialgebra and any Frobenius algebra, parameterized by elements of the Grothendieck-Teichmüller Lie algebra. We also prove that, for any given homotopy involutive Lie bialgebra structure in a vector space, there is an associated homotopy Batalin-Vilkovisky algebra structure on the associated Chevalley-Eilenberg complex.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
