Some algorithmic problems for Poisson algebras

Standard

Some algorithmic problems for Poisson algebras. / Zhang, Zerui; Chen, Yuqun; Bokut, Leonid A.

In: Journal of Algebra, Vol. 525, 01.05.2019, p. 562-588.

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

Harvard

Zhang, Z, Chen, Y & Bokut, LA 2019, 'Some algorithmic problems for Poisson algebras', Journal of Algebra, vol. 525, pp. 562-588. https://doi.org/10.1016/j.jalgebra.2019.02.001

APA

Zhang, Z., Chen, Y., & Bokut, L. A. (2019). Some algorithmic problems for Poisson algebras. Journal of Algebra, 525, 562-588. https://doi.org/10.1016/j.jalgebra.2019.02.001

Vancouver

Zhang Z, Chen Y, Bokut LA. Some algorithmic problems for Poisson algebras. Journal of Algebra. 2019 May 1;525:562-588. doi: 10.1016/j.jalgebra.2019.02.001

Author

Zhang, Zerui ; Chen, Yuqun ; Bokut, Leonid A. / Some algorithmic problems for Poisson algebras. In: Journal of Algebra. 2019 ; Vol. 525. pp. 562-588.

BibTeX

@article{0def2cfed1934fa78a4c861dda4c62c9,

title = "Some algorithmic problems for Poisson algebras",

abstract = "We develop a new theory of Gr{\"o}bner–Shirshov bases for Poisson algebras, which requires to introduce several nontrivial new techniques. As applications, we solve the word problem for finitely presented Poisson algebras in the case of a single relation with a leading monomial of Lie type and in the case when enough relations involve the Poisson bracket of generators.",

keywords = "Gr{\"o}bner–Shirshov basis, Poisson algebra, Word problem, GROBNER-SHIRSHOV BASES, Grobner-Shirshov basis",

author = "Zerui Zhang and Yuqun Chen and Bokut, {Leonid A.}",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = may,

day = "1",

doi = "10.1016/j.jalgebra.2019.02.001",

language = "English",

volume = "525",

pages = "562--588",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Some algorithmic problems for Poisson algebras

AU - Zhang, Zerui

AU - Chen, Yuqun

AU - Bokut, Leonid A.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - We develop a new theory of Gröbner–Shirshov bases for Poisson algebras, which requires to introduce several nontrivial new techniques. As applications, we solve the word problem for finitely presented Poisson algebras in the case of a single relation with a leading monomial of Lie type and in the case when enough relations involve the Poisson bracket of generators.

AB - We develop a new theory of Gröbner–Shirshov bases for Poisson algebras, which requires to introduce several nontrivial new techniques. As applications, we solve the word problem for finitely presented Poisson algebras in the case of a single relation with a leading monomial of Lie type and in the case when enough relations involve the Poisson bracket of generators.

KW - Gröbner–Shirshov basis

KW - Poisson algebra

KW - Word problem

KW - GROBNER-SHIRSHOV BASES

KW - Grobner-Shirshov basis

UR - http://www.scopus.com/inward/record.url?scp=85061427215&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2019.02.001

DO - 10.1016/j.jalgebra.2019.02.001

M3 - Article

AN - SCOPUS:85061427215

VL - 525

SP - 562

EP - 588

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 18563077