Scholarlink

<p>In this paper, we obtain the notion of an extended Rota-Baxter operator that generalizes the Rota-Baxter operator and the modified Rota-Baxter operator on Leibniz algebras, and give examples and general properties of extended Rota-Baxter operators. Next, we define a representation theory of extended Rota-Baxter Leibniz algebras and construct a cohomology theory. Furthermore, we justify this cohomology theory by interpreting lower degree cohomology groups as formal deformations of extended Rota-Baxter Leibniz algebras. Finally, we study non-abelian extensions of an extended Rota-Baxter Leibniz algebra by another extended Rota-Baxter Leibniz algebra, and we consider abelian extensions of extended Rota-Baxter Leibniz algebras as a particular case of non-abelian extensions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Extended Rota-Baxter Operators on Leibniz Algebras

  • 期刊论文

  • 发表日期：

    2025年1月5日

查看全文
  • Yizheng Li,
  • Dingguo Wang

摘要

In this paper, we obtain the notion of an extended Rota-Baxter operator that generalizes the Rota-Baxter operator and the modified Rota-Baxter operator on Leibniz algebras, and give examples and general properties of extended Rota-Baxter operators. Next, we define a representation theory of extended Rota-Baxter Leibniz algebras and construct a cohomology theory. Furthermore, we justify this cohomology theory by interpreting lower degree cohomology groups as formal deformations of extended Rota-Baxter Leibniz algebras. Finally, we study non-abelian extensions of an extended Rota-Baxter Leibniz algebra by another extended Rota-Baxter Leibniz algebra, and we consider abelian extensions of extended Rota-Baxter Leibniz algebras as a particular case of non-abelian extensions.