Rota-Baxter Lie 2-algebras

2022/03/07 by Zhang, Shilong, Liu, Jiefeng
#17B38 #18N25 #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.03403

Abstract

In this paper, we introduce the notion of Rota-Baxter Lie 2-algebras, which is a categorification of Rota-Baxter Lie algebras. We prove that the category of Rota-Baxter Lie 2-algebras and the category of 2-term Rota-Baxter L_∞-algebras are equivalent. We introduce the notion of a crossed module of Rota-Baxter Lie algebras and show that there is a one-to-one correspondence between strict 2-term Rota-Baxter L_∞-algebras and crossed modules of Rota-Baxter Lie algebras. We give the construction of crossed modules of Lie algebras from crossed modules of Rota-Baxter Lie algebras.

Related

• Extending structures of Rota-Baxter Lie algebras
• Matched pairs of Lie algebras and Rota-Baxter Lie algebras
• Rota-Baxter operators on crossed modules of Lie groups and categorical solutions of the Yang-Baxter equation
• Formal integration of complete Rota-Baxter Lie algebras
• Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras