Freely Generated Vertex Algebras and Non?Linear Lie Conformal Algebras
Copyright policy )Freely Generated Vertex Algebras and Non?Linear Lie Conformal Algebras
We introduce the notion of a non--linear Lie conformal superalgebra and prove a PBW theorem for its universal enveloping vertex algebra. We also show that conversely any graded freely generated vertex algebra is the universal enveloping algebra of a non--linear Lie conformal superalgebra. This correspondence will be applied in the subsequent work to the problem of classification of finitely generated simple graded vertex algebras.
38 pages
Nonlinear Sciences - Exactly Solvable and Integrable Systems, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Conformal algebras; vertex algebras; infinite dimensional Lie algebras, FOS: Physical sciences, vertex algebras, Mathematical Physics (math-ph), universal enveloping algebra, conformal algebras, superalgebra, Exactly Solvable and Integrable Systems (nlin.SI), Vertex operators; vertex operator algebras and related structures, Mathematical Physics
Nonlinear Sciences - Exactly Solvable and Integrable Systems, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Conformal algebras; vertex algebras; infinite dimensional Lie algebras, FOS: Physical sciences, vertex algebras, Mathematical Physics (math-ph), universal enveloping algebra, conformal algebras, superalgebra, Exactly Solvable and Integrable Systems (nlin.SI), Vertex operators; vertex operator algebras and related structures, Mathematical Physics
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