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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2015 Volume 98, Issue 5, Pages 756–768 (Mi mzm10895)

This article is cited in 1 paper

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.

UDC: 512.667.7

Received: 15.10.2013
Revised: 06.03.2015

DOI: 10.4213/mzm10895


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

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