Extensions and automorphisms of Rota-Baxter groups

被引：5

作者：

Das, Apurba ^{[1
]}

Rathee, Nishant ^{[2
]}

机构：

[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, W Bengal, India

[2] Harish Chandra Res Inst, CI Homi Bhabha Natl Inst, Chhatnag Rd, Prayagraj 211019, India

来源：

JOURNAL OF ALGEBRA | 2023年 / 636卷

关键词：

Rota-Baxter group; Skew braces; Extensions; Cohomology; Automorphisms; OPERATORS; COHOMOLOGY; ALGEBRAS; BRACES;

D O I：

10.1016/j.jalgebra.2023.09.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The notion of Rota-Baxter groups was recently introduced by Guo, Lang and Sheng [19] in the geometric study of Rota Baxter Lie algebras. They are closely related to skew braces as observed by Bardakov and Gubarev. In this paper, we study extensions of Rota-Baxter groups by constructing suitable cohomology theories. Among others, we find relations with the extensions of skew braces. Given an extension of Rota-Baxter groups, we also construct a short exact sequence connecting various automorphism groups, which generalizes the Wells short exact sequence.(c) 2023 Elsevier Inc. All rights reserved.

引用

页码：626 / 665

页数：40

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