论文标题
某些有限类别代数的霍奇柴尔德共同体作为简单
Hochschild cohomology of some finite category algebras as simplicial cohomology
论文作者
论文摘要
由于Gerstenhaber和Schack的结果，简单的共同体学环$ h^*（\ Mathcal {C}; k）$ poset $ \ Mathcal {c} $与Hochschild cohomology coohomology ring $ hh^*（k \ nathcal {c} $ s of the n permorphic of HochsChild cohomology grom of the Mathcal {c} $ a $ POSET被视为类别，$ K $是一个字段。 Mishchenko [6]的扩展结果，在类别$ \ MATHCAL {C} $的某些假设下，我们构造一个类别$ \ Mathcal {d} $和一个分级的$ K $ - linear isomorphism $ hh^*（k \ Mathcal {c}）解释学位一号的同胞学，我们还展示了$ k $ k $ -k \ Mathcal {c} $上的$ k $空间，某些半群级分级，对应于$ \ mathcal {d} $上的$ k $ - space-space。
By a result of Gerstenhaber and Schack the simplicial cohomology ring $H^*(\mathcal{C};k)$ of a poset $\mathcal{C}$ is isomorphic to the Hochschild cohomology ring $HH^*(k\mathcal{C})$ of the category algebra $k\mathcal{C}$, where the poset is viewed as a category and $k$ is a field. Extending results of Mishchenko [6], under certain assumptions on a category $\mathcal{C}$, we construct a category $\mathcal{D}$ and a graded $k$-linear isomorphism $HH^*(k\mathcal{C})\cong H^*(\mathcal{D}; k)$. Interpreting the degree one cohomology, we also show how the $k$-space of derivations on $k\mathcal{C}$, graded by some semigroup, corresponds to the $k$-space of characters on $\mathcal{D}$.
