论文标题
对称的共同体学和对称的Hochschild共同共同共同共同霍普夫代数
Symmetric cohomology and symmetric Hochschild cohomology of cocommutative Hopf algebras
论文作者
论文摘要
StaiC定义了组的对称共同体，并研究了次级对称的共同体学组对应于组扩展和从对称共同体到经典共同体学的规范图的注入性。在本文中，我们定义了对称的共同霍基柴尔德共同体，用于共同交流的Hopf代数。第一个是对群体的对称共同体的概括。我们给出了对称的共同体学和对称的霍基柴尔德共同体之间的同构，这是Eilenberg-Maclane的经典结果的对称版本，以及Ginzburg-kumar的Hopf代数。此外，要考虑对称同谋与经典的共同体相吻合的条件，我们研究了一种分辨率的预测性，该分辨率提供了对称的共同体学。
Staic defined symmetric cohomology of groups and studied that the secondary symmetric cohomology group is corresponding to group extensions and the injectivity of the canonical map from symmetric cohomology to classical cohomology. In this paper, we define symmetric cohomology and symmetric Hochschild cohomology for cocommutative Hopf algebras. The first one is a generalization of symmetric cohomology of groups. We give an isomorphism between symmetric cohomology and symmetric Hochschild cohomology, which is a symmetric version of the classical result about cohomology of groups by Eilenberg-MacLane and cohomology of Hopf algebras by Ginzburg-Kumar. Moreover, to consider the condition that symmetric cohomology coincides with classical cohomology, we investigate the projectivity of a resolution which gives symmetric cohomology.
