Inverse semigroup cohomology and crossed module extensions of semilattices of groups by inverse semigroups

被引：0

作者：

Dokuchaev, Mikhailo ^{[1
]}

Khrypchenko, Mykola ^{[2
]}

Makuta, Mayumi ^{[1
]}

机构：

[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil

[2] Univ Fed Santa Catarina, Dept Matemat, Campus Reitor Joao David Ferreira Lima, BR-88040900 Florianopolis, SC, Brazil

来源：

JOURNAL OF ALGEBRA | 2022年 / 593卷

基金：

巴西圣保罗研究基金会;

关键词：

Crossed module; Crossed module extension; Cohomology; Inverse semigroup; Semilattice of groups; F -inverse monoid; MONOIDS; COEFFICIENTS;

D O I：

10.1016/j.jalgebra.2021.11.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define and study the notion of a crossed module over an inverse semigroup and the corresponding 4-term exact sequences, called crossed module extensions. For a crossed module A over an F-inverse monoid T, we show that equivalence classes of admissible crossed module extensions of A by T are in a one-to-one correspondence with the elements of the cohomology group H3 <=(T1, A1). (c) 2021 Elsevier Inc. All rights reserved.

引用

页码：341 / 397

页数：57

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