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Mat. Zametki, 2015, Volume 98, Issue 5, Pages 756–768 (Mi mz10895)  

Spectral Sequence and Finitely Presented Dimension for Weak Hopf–Galois Extensions

X. Y. Zhou, T. Yang

Nanjing Agricultural University, China

Abstract: Let $H$ be a weak Hopf algebra, $A$ a right weak $H$-comodule algebra, and $B$ the subalgebra of the $H$-coinvariant elements of $A$. Let $A/B$ be a right weak $H$-Galois extension. In this paper, a spectral sequence for $\operatorname{Ext}$ which yields an estimate for the global dimension of $A$ in terms of the corresponding data for $H$ and $B$ is constructed. Next, the relationship between the finitely presented dimensions of $A$ and its subalgebra $B$ are given. Further, the case in which $A$ is an $n$-Gorenstein algebra is studied.

Keywords: weak Hopf–Galois extension, spectral sequence, finitely presented dimension, Gorenstein algebra.

Funding Agency Grant Number
Фонд фундаментальных исследований центральных университетов KYZ201322


DOI: https://doi.org/10.4213/mzm10895

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English version:
Mathematical Notes, 2015, 98:5, 820–830

Bibliographic databases:

UDC: 512.667.7
Received: 15.10.2013
Revised: 06.03.2015

Citation: X. Y. Zhou, T. Yang, “Spectral Sequence and Finitely Presented Dimension for Weak Hopf–Galois Extensions”, Mat. Zametki, 98:5 (2015), 756–768; Math. Notes, 98:5 (2015), 820–830

Citation in format AMSBIB
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