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The Superalgebras of Jordan Brackets Defined by the n-Dimensional Sphere. / Zhelyabin, V. N.; Zakharov, A. S.
в: Siberian Mathematical Journal, Том 61, № 4, 01.07.2020, стр. 632-647.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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