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Modified Rota-Baxter Lie-Yamaguti algebras

Wen Teng, Shuangjian Guo

Abstract

In this paper, first we introduce the concept of modified Rota-Baxter Lie-Yamaguti algebras. Then the cohomology of a modified Rota-Baxter Lie-Yamaguti algebra with coefficients in a suitable representation is established. As applications, the formal deformations and abelian extensions of modified Rota-Baxter Lie-Yamaguti algebras are studied using the second cohomology group.

Modified Rota-Baxter Lie-Yamaguti algebras

Abstract

In this paper, first we introduce the concept of modified Rota-Baxter Lie-Yamaguti algebras. Then the cohomology of a modified Rota-Baxter Lie-Yamaguti algebra with coefficients in a suitable representation is established. As applications, the formal deformations and abelian extensions of modified Rota-Baxter Lie-Yamaguti algebras are studied using the second cohomology group.
Paper Structure (7 sections, 16 theorems, 72 equations)

This paper contains 7 sections, 16 theorems, 72 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Modified Rota-Baxter Lie-Yamaguti algebras
  4. Representations of modified Rota-Baxter Lie-Yamaguti algebras
  5. Cohomology of modified Rota-Baxter Lie-Yamaguti algebras
  6. Formal deformations of modified Rota-Baxter Lie-Yamaguti algebras
  7. Abelian extensions of modified Rota-Baxter Lie-Yamaguti algebras

Key Result

Proposition 3.8

Let $(\mathfrak{L}, [-, -], \{-, -, -\})$ be a Lie-Yamaguti algebra. A linear map $R$ is a modified Rota-Baxter operator if and only if $-R$ is also a modified Rota-Baxter operator.

Theorems & Definitions (61)

  • Definition 2.1
  • Example 2.2
  • Example 2.3
  • Example 2.4
  • Example 2.5
  • Example 2.6
  • Definition 2.7
  • Definition 2.8
  • Definition 2.9
  • Example 2.10
  • ...and 51 more