论文标题
（CO）γ组和γ-同源代数的同源性
(Co)homology of Γ-groups and Γ-homological algebra
论文作者
论文摘要
这是对我们在γ-肌电组的同源性环境中，特别是γ-等级同源性的同源性的同源性和γ组同源性的同源代数的方法的进一步研究。这种方法可以称为γ-论代数。非亚伯式扩展的抽象核与非亚伯扩展的障碍和第二组共同体的障碍的关系扩展到了非亚伯γ延伸的情况。我们计算有限环状γ组的有理γ-等值式（CO）同源组。 goγ-模块A与Aγ组g的n倍量度扩展的同构延伸，其g的（n+1）Thγ-等值群体与A的系数在A中的同胞相结合。当γ对Hochschild复合物的作用是由于其对基本环的作用引起的，其中包含γ组的γequivariant（CO）同源性。建立了与Kahler差异，Morita等价和衍生功能有关的γ-等级Hochschild同源性的重要特性。通过使用相关派生函数引入和研究了交叉γ模块的组（CO）同源性和γ-等级组（CO）同源性，最终给出了代数K理论，通勤环的GALOIS理论的应用和组的共同学位。
This is a further investigation of our approach to group actions in homological algebra in the settings of homology of Γ-simplicial groups, particularly of Γ-equivariant homology and cohomology of Γ-groups. This approach could be called Γ-homological algebra. The abstract kernel of non-abelian extensions of groups, its relation with the obstruction to the existence of non-abelian extensions and with the second group cohomology are extended to the case of non-abelian Γ-extensions of Γ-groups. We compute the rational Γ-equivariant (co)homology groups of finite cyclic Γ-groups. The isomorphism of the group of n-fold Γ-equivariant extensions of a Γ-group G by a G o Γ-module A with the (n+1)th Γ-equivariant group cohomology of G with coefficients in A is proven.We define the Γ-equivariant Hochschild homology as the homology of the Γ- Hochschild complex involving the cyclic homology when the basic ring contains rational numbers and generalizing the Γequivariant(co)homology of Γ-groups when the action of the group Γ on the Hochschild complex is induced by its action on the basic ring. Important properties of the Γ-equivariant Hochschild homology related to Kahler differentials, Morita equivalence and derived functors are established. Group (co)homology and Γ-equivariant group (co)homology of crossed Γ-modules are introduced and investigated by using relevant derived functors Finally, applications to algebraic K-theory, Galois theory of commutative rings and cohomological dimension of groups are given.
