Computation of cohomology of finite Lie conformal algebras

2025/09/09 by Zhenyu Zhang, Zhang, Zhenyu, Lamei Yuan +1
Computer Science · Mathematics · #17B56 #17B65 #17B68 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2509.07332

openalex publication_date 2025/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using the energy operator introduced by B. Bakalov, A. De Sole, and V. G. Kac, we propose an algorithm for computing the cohomology of finitely generated free Lie conformal algebras with a Virasoro element. This computational method enables us to determine cohomologies with coefficients in their conformal modules, including the trivial module, irreducible finitely free modules, and adjoint modules. As concrete applications, we compute by Mathematica both basic and reduced cohomologies for the W(b), Schrödinger-Virasoro and extended Schrödinger-Virasoro Lie conformal algebras.

Citations

• Twisting theory, relative Rota-Baxter type operators and L_∞-algebras on Lie conformal algebras
• Cohomology of the extended Schrödinger-Virasoro conformal algebra
• Cohomology of the Schrödinger-Virasoro conformal algebra
• Extensions of modules over a class of Lie conformal algebras W(b)
• Classification of finite irreducible conformal modules over a class of Lie conformal algebras of Block type
• Cohomology of Heisenberg-Virasoro conformal algebra
• Structures of W(2,2) Lie conformal algebra
• Conformal Modules

Related

• Cohomology of the extended Schrödinger-Virasoro conformal algebra
• Cohomology of the Schrödinger-Virasoro conformal algebra
• Cohomology of Heisenberg-Virasoro conformal algebra
• Finite irreducible modules of Lie conformal algebras W(a,b) and some Schrödinger-Virasoro type Lie conformal algebras
• Extensions of finite irreducible modules of Lie conformal algebras W(a,b) and some Schrödinger-Virasoro type Lie conformal algebras