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The Superalgebras of Jordan Brackets Defined by the n-Dimensional Sphere. / Zhelyabin, V. N.; Zakharov, A. S.

In: Siberian Mathematical Journal, Vol. 61, No. 4, 01.07.2020, p. 632-647.

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

Harvard

Zhelyabin, VN & Zakharov, AS 2020, 'The Superalgebras of Jordan Brackets Defined by the n-Dimensional Sphere', Siberian Mathematical Journal, vol. 61, no. 4, pp. 632-647. https://doi.org/10.1134/S0037446620040072

APA

Zhelyabin, V. N., & Zakharov, A. S. (2020). The Superalgebras of Jordan Brackets Defined by the n-Dimensional Sphere. Siberian Mathematical Journal, 61(4), 632-647. https://doi.org/10.1134/S0037446620040072

Vancouver

Zhelyabin VN, Zakharov AS. The Superalgebras of Jordan Brackets Defined by the n-Dimensional Sphere. Siberian Mathematical Journal. 2020 Jul 1;61(4):632-647. doi: 10.1134/S0037446620040072

Author

Zhelyabin, V. N. ; Zakharov, A. S. / The Superalgebras of Jordan Brackets Defined by the n-Dimensional Sphere. In: Siberian Mathematical Journal. 2020 ; Vol. 61, No. 4. pp. 632-647.

BibTeX

@article{4769dd05994d4bf9b8cdd0c9967045cf,
title = "The Superalgebras of Jordan Brackets Defined by the n-Dimensional Sphere",
abstract = "We study the generalized Leibniz brackets on the coordinatealgebra of the $ n $-dimensional sphere. In the case of the one-dimensionalsphere, we show that each of these is a bracket of vector type.Each Jordan bracket on the coordinatealgebra of the two-dimensional sphereis a generalized Poisson bracket. We equip the coordinate algebraof a sphere of odd dimension with a Jordan bracketwhose Kantor double is a simple Jordan superalgebra.Using such superalgebras, we provide some examplesof the simple abelian Jordan superalgebras whose odd part isa finitely generated projective module of rank 1in an arbitrary number of generators.An analogous result holds for theCartesian product of the sphere of even dimension and the affine line.In particular, in the case of the 2-dimensional spherewe obtain the exceptional Jordan superalgebra. Thesuperalgebras we constructed give new examples of simple Jordan superalgebras.",
keywords = "512.554, affine space, associative commutative superalgebra, bracket of vector type, derivation, differential algebra, Grassmann algebra, Jordan bracket, Jordan superalgebra, Poisson bracket, polynomial algebra, projective module, sphere, superalgebra of a bilinear form",
author = "Zhelyabin, {V. N.} and Zakharov, {A. S.}",
note = "Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd.",
year = "2020",
month = jul,
day = "1",
doi = "10.1134/S0037446620040072",
language = "English",
volume = "61",
pages = "632--647",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "4",

}

RIS

TY - JOUR

T1 - The Superalgebras of Jordan Brackets Defined by the n-Dimensional Sphere

AU - Zhelyabin, V. N.

AU - Zakharov, A. S.

N1 - Publisher Copyright: © 2020, Pleiades Publishing, Ltd.

PY - 2020/7/1

Y1 - 2020/7/1

N2 - We study the generalized Leibniz brackets on the coordinatealgebra of the $ n $-dimensional sphere. In the case of the one-dimensionalsphere, we show that each of these is a bracket of vector type.Each Jordan bracket on the coordinatealgebra of the two-dimensional sphereis a generalized Poisson bracket. We equip the coordinate algebraof a sphere of odd dimension with a Jordan bracketwhose Kantor double is a simple Jordan superalgebra.Using such superalgebras, we provide some examplesof the simple abelian Jordan superalgebras whose odd part isa finitely generated projective module of rank 1in an arbitrary number of generators.An analogous result holds for theCartesian product of the sphere of even dimension and the affine line.In particular, in the case of the 2-dimensional spherewe obtain the exceptional Jordan superalgebra. Thesuperalgebras we constructed give new examples of simple Jordan superalgebras.

AB - We study the generalized Leibniz brackets on the coordinatealgebra of the $ n $-dimensional sphere. In the case of the one-dimensionalsphere, we show that each of these is a bracket of vector type.Each Jordan bracket on the coordinatealgebra of the two-dimensional sphereis a generalized Poisson bracket. We equip the coordinate algebraof a sphere of odd dimension with a Jordan bracketwhose Kantor double is a simple Jordan superalgebra.Using such superalgebras, we provide some examplesof the simple abelian Jordan superalgebras whose odd part isa finitely generated projective module of rank 1in an arbitrary number of generators.An analogous result holds for theCartesian product of the sphere of even dimension and the affine line.In particular, in the case of the 2-dimensional spherewe obtain the exceptional Jordan superalgebra. Thesuperalgebras we constructed give new examples of simple Jordan superalgebras.

KW - 512.554

KW - affine space

KW - associative commutative superalgebra

KW - bracket of vector type

KW - derivation

KW - differential algebra

KW - Grassmann algebra

KW - Jordan bracket

KW - Jordan superalgebra

KW - Poisson bracket

KW - polynomial algebra

KW - projective module

KW - sphere

KW - superalgebra of a bilinear form

UR - http://www.scopus.com/inward/record.url?scp=85088790687&partnerID=8YFLogxK

U2 - 10.1134/S0037446620040072

DO - 10.1134/S0037446620040072

M3 - Article

AN - SCOPUS:85088790687

VL - 61

SP - 632

EP - 647

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -

ID: 24956573