Poisson Pseudoalgebras

2023/07/31 by Bojko Bakalov, Ju Wang, Bakalov, Bojko +1
Mathematics · Physics and Astronomy · #17B66 #18M70 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Primary 17B63 #Quantum Algebra (math.QA) #Secondary 17B65

paper · pdf · doi:10.48550/arxiv.2307.16388

openalex publication_date 2023/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any cocommutative Hopf algebra H and a left H-module V, we construct an operad P^cl_H(V), which in the special case when H is the algebra of polynomials in one variable reduces to the classical operad P^cl(V). Morphisms from the Lie operad to P^cl(V) correspond to Poisson vertex algebra structures on V. Likewise, our operad P^cl_H(V) gives rise to the notion of a Poisson pseudoalgebra; thus extending the notion of a Lie pseudoalgebra. As a byproduct of our construction, we introduce two cohomology theories for Poisson pseudoalgebras, generalizing the variational and classical cohomology of Poisson vertex algebras.

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