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

共 50 条

[41] Super module amenability of inverse semigroup algebras
M. Lashkarizadeh Bami
M. Valaei
M. Amini
Semigroup Forum, 2013, 86 : 279 - 288
[42] VON NEUMANN ALGEBRAS AND EXTENSIONS OF INVERSE SEMIGROUPS
Donsig, Allan P.
Fuller, Adam H.
Pitts, David R.
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2017, 60 (01) : 57 - 97
[43] On embeddability of idempotent separating extensions of inverse semigroups
Billhardt, B
Szittyai, I
SEMIGROUP FORUM, 2000, 61 (01) : 26 - 31
[44] Finite presentability of HNN extensions of inverse semigroups
Dombi, ER
Gilbert, ND
Ruskuc, N
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2005, 15 (03) : 423 - 436
[45] On Embeddability of Idempotent Separating Extensions of Inverse Semigroups
Bernd Billhardt
István Szittyai
Semigroup Forum, 2000, 61 : 26 - 31
[46] Locally full HNN extensions of inverse semigroups
Yamamura, A
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 2001, 70 : 235 - 272
[47] Semigroup closures of finite rank symmetric inverse semigroups
Oleg Gutik
Jimmie Lawson
Dušan Repovš
Semigroup Forum, 2009, 78
[48] Semigroup closures of finite rank symmetric inverse semigroups
Gutik, Oleg
Lawson, Jimmie
Repovs, Dusan
SEMIGROUP FORUM, 2009, 78 (02) : 326 - 336
[49] Embedding theorems for HNN extensions of inverse semigroups
Yamamura, Akihiro
JOURNAL OF PURE AND APPLIED ALGEBRA, 2007, 210 (02) : 521 - 536
[50] Extensions of Clifford subsemigroups of the finite symmetric inverse semigroup
Yang, XL
COMMUNICATIONS IN ALGEBRA, 2005, 33 (02) : 381 - 391

← 1 2 3 4 5 →