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The third partial cohomology group and existence of extensions of semilattices of groups by groups

被引：1
|
作者：
Dokuchaev, Mikhailo [3 ]
Khrypchenko, Mykola [1 ,2 ]
Makuta, Mayumi [3 ]
机构：
[1] Univ Fed Santa Catarina, Dept Matemat, Campus Reitor Joao David Ferreira Lima, BR-88040900 Florianopolis, SC, Brazil
[2] Univ Nova Lisboa, Ctr Matemat & Aplicacoes, Fac Ciencias & Tecnol, P-2829516 Caparica, Portugal
[3] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil
来源：
FORUM MATHEMATICUM | 2020年 / 32卷 / 05期
基金：
巴西圣保罗研究基金会;
关键词：
Partial group action; partial cohomology; obstruction; extension; inverse semigroup; TWISTED PARTIAL ACTIONS; CROSSED-PRODUCTS;
D O I：
10.1515/forum-2019-0281
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce the concept of a partial abstract kernel associated to a group G and a semilattice of groups A and relate the partial cohomology group H-3 (G, C(A)) with the obstructions to the existence of admissible extensions of A by G which realize the given abstract kernel. We also show that if such extensions exist, then they are classified by H-2 (G, C(A)).
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页码：1297 / 1313
页数：17
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