Universal enveloping algebra of a pair of compatible Lie brackets

Standard

Universal enveloping algebra of a pair of compatible Lie brackets. / Gubarev, Vsevolod.

In: International Journal of Algebra and Computation, Vol. 32, No. 7, 01.11.2022, p. 1335-1344.

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

Harvard

Gubarev, V 2022, 'Universal enveloping algebra of a pair of compatible Lie brackets', International Journal of Algebra and Computation, vol. 32, no. 7, pp. 1335-1344. https://doi.org/10.1142/S0218196722500588

APA

Gubarev, V. (2022). Universal enveloping algebra of a pair of compatible Lie brackets. International Journal of Algebra and Computation, 32(7), 1335-1344. https://doi.org/10.1142/S0218196722500588

Vancouver

Gubarev V. Universal enveloping algebra of a pair of compatible Lie brackets. International Journal of Algebra and Computation. 2022 Nov 1;32(7):1335-1344. doi: 10.1142/S0218196722500588

Author

Gubarev, Vsevolod. / Universal enveloping algebra of a pair of compatible Lie brackets. In: International Journal of Algebra and Computation. 2022 ; Vol. 32, No. 7. pp. 1335-1344.

BibTeX

@article{8bfd39130d2842f58c8b94889a264ade,

title = "Universal enveloping algebra of a pair of compatible Lie brackets",

abstract = "By applying the Poincar{\'e} - Birkhoff - Witt property and the Gr{\"o}bner - Shirshov bases technique, we find the linear basis of the associative universal enveloping algebra in the sense of Ginzburg and Kapranov of a pair of compatible Lie brackets. We state that the growth rate of this universal enveloping over n-dimensional compatible Lie algebra equals n + 1. ",

keywords = "compatible Lie brackets, growth rate, Gr{\"o}bner - Shirshov basis, Universal enveloping algebra over an operad",

author = "Vsevolod Gubarev",

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

year = "2022",

month = nov,

day = "1",

doi = "10.1142/S0218196722500588",

language = "English",

volume = "32",

pages = "1335--1344",

journal = "International Journal of Algebra and Computation",

issn = "0218-1967",

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

number = "7",

}

RIS

TY - JOUR

T1 - Universal enveloping algebra of a pair of compatible Lie brackets

AU - Gubarev, Vsevolod

PY - 2022/11/1

Y1 - 2022/11/1

N2 - By applying the Poincaré - Birkhoff - Witt property and the Gröbner - Shirshov bases technique, we find the linear basis of the associative universal enveloping algebra in the sense of Ginzburg and Kapranov of a pair of compatible Lie brackets. We state that the growth rate of this universal enveloping over n-dimensional compatible Lie algebra equals n + 1.

AB - By applying the Poincaré - Birkhoff - Witt property and the Gröbner - Shirshov bases technique, we find the linear basis of the associative universal enveloping algebra in the sense of Ginzburg and Kapranov of a pair of compatible Lie brackets. We state that the growth rate of this universal enveloping over n-dimensional compatible Lie algebra equals n + 1.

KW - compatible Lie brackets

KW - growth rate

KW - Gröbner - Shirshov basis

KW - Universal enveloping algebra over an operad

UR - http://www.scopus.com/inward/record.url?scp=85136237535&partnerID=8YFLogxK

U2 - 10.1142/S0218196722500588

DO - 10.1142/S0218196722500588

M3 - Article

AN - SCOPUS:85136237535

VL - 32

SP - 1335

EP - 1344

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 7

ER -

ID: 36958150