Lie 2-bialgebras

Abstract

In this paper, we study Lie 2-bialgebras, with special attention to coboundary ones, with the help of the cohomology theory of $L_{\infty }$-algebras with coefficients in $L_{\infty }$-modules. We construct examples of strict Lie 2-bialgebras from left-symmetric algebras and symplectic Lie algebras.

22 pages

References in corpus (4)

• A Unified Algebraic Approach to Classical Yang-Baxter Equation
• Left-symmetric Bialgebras and An Analogue of the Classical Yang-Baxter Equation
• On weak Lie 2-algebras
• Weak Lie 2-bialgebra

Cited by in corpus (13)

• Deformations of Lie 2-algebras
• Infinitesimal 2-braidings and differential crossed modules
• Cohomological characterizations of non-abelian extensions of strict Lie 2-algebras
• (2-)Drinfel'd Double and (2-)BF Theory
• Higher Gauge Theory and Integrability
• Infinitesimal 2-braidings from 2-shifted Poisson structures
• 2-Drinfel'd double symmetry of the 4d Kitaev model
• Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
• A cohomology theory for Lie 2-algebras
• Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules
• Cohomology of hemistrict Lie 2-algebras
• Manin triples on multiplicative Courant algebroids
• Shifted Poisson structures on higher Chevalley-Eilenberg algebras