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- Title
Quadratic Lie conformal superalgebras related to Novikov superalgebras.
- Authors
Kolesnikov, Pavel S.; Kozlov, Roman A.; Panasenko, Aleksander S.
- Abstract
We study quadratic Lie conformal superalgebras associated with Novikov superalgebras. For every Novikov superalgebra (V,o), we construct an enveloping differential Poisson superalgebra U(V) with a derivation d such that u o v D ud(v) and {u, v} = u o v -(-1)|u||v|v o u for u, v ∈ V. The latter means that the commutator Gelfand-Dorfman superalgebra of V is special. Next, we prove that every quadratic Lie conformal superalgebra constructed on a finite-dimensional special Gelfand-Dorfman superalgebra has a finite faithful conformal representation. This statement is a step towards a solution of the following open problem: whether a finite Lie conformal (super)algebra has a finite faithful conformal representation.
- Subjects
SUPERALGEBRAS; NONASSOCIATIVE algebras; NOVIKOV conjecture; ABSTRACT algebra; QUADRATIC differentials
- Publication
Journal of Noncommutative Geometry, 2021, Vol 15, Issue 4, p1485
- ISSN
1661-6952
- Publication type
Article
- DOI
10.4171/JNCG/445