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Hopf dense Galois extensions and applications
张印火 教授(比利时Hasselt大学)
2018-01-01 12:13  华东师范大学

曹锡华数学论坛

报告人简介:
Hopf代数和Hopf Galois扩张理论国际知名专家,1991年在比利时获得博士学位,后在新西兰和比利时任教授。现为比利时Hasselt大学终身教授,曾在国际上多次组织Hopf代数与Tensor Categories国际会议。

报告内容简介:
Let $H$ be a finite dimensional Hopf algebra, and let $A$ be a left $H$-module algebra. Motivated by the study of the isolated singularities of $A^H$ and the endomorphism ring $\End_{A^H}(A)$, we introduce the concept of dense Galois extensions consists of the so-called densely group graded algebras, which are weaker versions of strongly graded algebras. A weaker version of Dade's Theorem holds for densely group graded algebras. As applications, we recover the classical equivalence of the noncommutative projective scheme over a noetherian $\mathbb{N}$-graded algebra $A$ and its $d$-th Veronese subalgebra $A^{(d)}$ respectively. Hopf dense Galois extensions are also applied to the study of noncommuative graded isolated singularities.

主持人:胡乃红 教授