On the structure of finite Novikov conformal algebras

2026/06/30 by Pavel Kolesnikov, Jiefeng Liu
#math.RA

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Abstract

We classify finite simple Novikov conformal algebras over an algebraically closed field of characteristic zero. The classification consists of the current conformal algebra over the base field and a one-parameter list of Virasoro-like conformal algebras. A semisimple finite Novikov conformal algebra is proved to be a direct sum of simple ones. We also describe deformations and central extensions of finite simple Novikov conformal algebras.

Citations

• Differential envelopes of Novikov conformal algebras
• Cohomology and deformation quantization of Poisson conformal algebras
• Left-symmetric conformal algebras and vertex algebras
• Simple Jordan conformal superalgebras
• Structure theory of finite Lie conformal superalgebras
• On the classification of subalgebras of Cend_N and gc_N
• Classifications of Simple Novikov Algebras and Their Irreducible Modules of Characteristic 0
• Quadratic conformal superalgebras
• On free conformal and vertex algebras
• Formal distribution algebras and conformal algebras
• Koszul duality for operads

Related

• Differential envelopes of Novikov conformal algebras
• Extensions of conformal modules
• Classifications of Simple Novikov Algebras and Their Irreducible Modules of Characteristic 0
• Conformal modules and their extensions of a Lie conformal algebra related to a 2-dimensional Novikov algebra
• Quadratic conformal superalgebras