Shifted Poisson structures on higher Chevalley–Eilenberg algebras
Abstract
Abstract This paper develops a graphical calculus to determine the n -shifted Poisson structures on finitely generated semi-free commutative differential graded algebras. When applied to the Chevalley–Eilenberg algebra of an ordinary Lie algebra, we recover Safronov’s result that the $$(n=1)$$ ( n = 1 ) - and $$(n=2)$$ ( n = 2 ) -shifted Poisson structures in this case are given by quasi-Lie bialgebra structures and, respectively, invariant symmetric tensors. We generalize these results to the Chevalley–Eilenberg algebra of a Lie 2-algebra and obtain $$n\in \{1,2,3,4\}$$ n ∈ { 1 , 2 , 3 , 4 } shifted Poisson structures in this case, which we interpret as semi-classical data of ‘higher quantum groups’.
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Letters in Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 116
- Issue
- 1
- Pages
- 19–19
- Publication date
- 18 February 2026
- Language
- EN