Defining relations and Gröbner-Shirshov bases of Poisson algebras as of conformal modules

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Defining relations and Gröbner-Shirshov bases of Poisson algebras as of conformal modules. / Kolesnikov, Pavel S.; Panasenko, A. S.

In: Journal of Algebra and its Applications, Vol. 21, No. 7, 2250138, 01.07.2022.

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

BibTeX

@article{ae24e03fa5e749a796b0877b8d74515b,

title = "Defining relations and Gr{\"o}bner-Shirshov bases of Poisson algebras as of conformal modules",

abstract = "We study the relation between Poisson algebras and representations of Lie conformal algebras. We establish a Gr{\"o}bner-Shirshov basis theory framework for modules over associative conformal algebras and apply this technique to Poisson algebras considered as conformal modules over appropriate associative conformal envelopes of current Lie conformal algebras. As a result, we obtain a setting for the calculation of a Gr{\"o}bner-Shirshov basis in a Poisson algebra.",

keywords = "Conformal algebra, Gr{\"o}bner-Shirshov basis, Poisson algebra",

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

note = "Publisher Copyright: {\textcopyright} 2022 World Scientific Publishing Company.",

year = "2022",

month = jul,

day = "1",

doi = "10.1142/S0219498822501389",

language = "English",

volume = "21",

journal = "Journal of Algebra and its Applications",

issn = "0219-4988",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "7",

}

RIS

TY - JOUR

T1 - Defining relations and Gröbner-Shirshov bases of Poisson algebras as of conformal modules

AU - Kolesnikov, Pavel S.

AU - Panasenko, A. S.

PY - 2022/7/1

Y1 - 2022/7/1

N2 - We study the relation between Poisson algebras and representations of Lie conformal algebras. We establish a Gröbner-Shirshov basis theory framework for modules over associative conformal algebras and apply this technique to Poisson algebras considered as conformal modules over appropriate associative conformal envelopes of current Lie conformal algebras. As a result, we obtain a setting for the calculation of a Gröbner-Shirshov basis in a Poisson algebra.

AB - We study the relation between Poisson algebras and representations of Lie conformal algebras. We establish a Gröbner-Shirshov basis theory framework for modules over associative conformal algebras and apply this technique to Poisson algebras considered as conformal modules over appropriate associative conformal envelopes of current Lie conformal algebras. As a result, we obtain a setting for the calculation of a Gröbner-Shirshov basis in a Poisson algebra.

KW - Conformal algebra

KW - Gröbner-Shirshov basis

KW - Poisson algebra

UR - http://www.scopus.com/inward/record.url?scp=85103473073&partnerID=8YFLogxK

U2 - 10.1142/S0219498822501389

DO - 10.1142/S0219498822501389

M3 - Article

AN - SCOPUS:85103473073

VL - 21

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

SN - 0219-4988

IS - 7

M1 - 2250138

ER -

ID: 28256071