论文标题
代数图
Operations on the Hochschild Bicomplex of a Diagram of Algebras
论文作者
论文摘要
代数图是一个值得一类的联想代数的函子。我构建了作用于代数图的霍基柴尔德双学术上的作战。我直接证明了使用该奥尔赛车的霍基柴尔德共同体，代数是Gerstenhaber代数。我还表明，总的综合体是$ l_ \ infty $ -Algebra。对于减少和阿斯尼亚的亚复合物和Asimplicial的共同体学也是如此。该结构通过Maurer-Cartan方程来控制代数图的图形。
A diagram of algebras is a functor valued in a category of associative algebras. I construct an operad acting on the Hochschild bicomplex of a diagram of algebras. Using this operad, I give a direct proof that the Hochschild cohomology of a diagram of algebras is a Gerstenhaber algebra. I also show that the total complex is an $L_\infty$-algebra. The same results are true for the reduced and asimplicial subcomplexes and asimplicial cohomology. This structure governs deformations of diagrams of algebras through the Maurer-Cartan equation.
