Quadratic Lie conformal superalgebras related to Novikov superalgebras

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Quadratic Lie conformal superalgebras related to Novikov superalgebras. / Kolesnikov, Pavel S.; Kozlov, Roman A.; Panasenko, Aleksander S.

In: Journal of Noncommutative Geometry, Vol. 15, No. 4, 2021, p. 1485-1500.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{eb42daa93e16486cae419301f7519b5a,

title = "Quadratic Lie conformal superalgebras related to Novikov superalgebras",

abstract = "We study quadratic Lie conformal superalgebras associated with Novikov superalgebras. For every Novikov superalgebra.V; ı/, we construct an enveloping differential Poisson superalgebra U.V/with a derivation d such that u o v = ud(v) and 1u; v} u o v -.(-1)|u||v| vo 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.",

keywords = "Conformal superalgebra, Gelfand-Dorfman superalgebra, Novikov superalgebra, Poisson superalgebra",

author = "Kolesnikov, {Pavel S.} and Kozlov, {Roman A.} and Panasenko, {Aleksander S.}",

note = "Funding Information: Funding. Research supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: {\textcopyright} 2021 European Mathematical Society Published by EMS Press This work is licensed under a CC BY 4.0 license",

year = "2021",

doi = "10.4171/JNCG/445",

language = "English",

volume = "15",

pages = "1485--1500",

journal = "Journal of Noncommutative Geometry",

issn = "1661-6952",

publisher = "European Mathematical Society Publishing House",

number = "4",

}

RIS

TY - JOUR

T1 - Quadratic Lie conformal superalgebras related to Novikov superalgebras

AU - Kolesnikov, Pavel S.

AU - Kozlov, Roman A.

AU - Panasenko, Aleksander S.

N1 - Funding Information: Funding. Research supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2021 European Mathematical Society Published by EMS Press This work is licensed under a CC BY 4.0 license

PY - 2021

Y1 - 2021

N2 - We study quadratic Lie conformal superalgebras associated with Novikov superalgebras. For every Novikov superalgebra.V; ı/, we construct an enveloping differential Poisson superalgebra U.V/with a derivation d such that u o v = ud(v) and 1u; v} u o v -.(-1)|u||v| vo 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.

AB - We study quadratic Lie conformal superalgebras associated with Novikov superalgebras. For every Novikov superalgebra.V; ı/, we construct an enveloping differential Poisson superalgebra U.V/with a derivation d such that u o v = ud(v) and 1u; v} u o v -.(-1)|u||v| vo 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.

KW - Conformal superalgebra

KW - Gelfand-Dorfman superalgebra

KW - Novikov superalgebra

KW - Poisson superalgebra

UR - http://www.scopus.com/inward/record.url?scp=85123776817&partnerID=8YFLogxK

U2 - 10.4171/JNCG/445

DO - 10.4171/JNCG/445

M3 - Article

AN - SCOPUS:85123776817

VL - 15

SP - 1485

EP - 1500

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 4

ER -

ID: 35386021