IDEALS OF GENERAL LINEAR LIE ALGEBRAS OF INFINITE-DIMENSIONAL VECTOR SPACES

被引：1

作者：

Bezushchak, Oksana ^{[1
]}

Holubowski, Waldemar ^{[2
]}

Oliynyk, Bogdana ^{[2
,3
]}

机构：

[1] Taras Shevchenko Natl Univ, Fac Mech & Math, Volodymyrska 60, UA-01033 Kiev, Ukraine

[2] Silesian Tech Univ, Fac Appl Math, Kaszubska 23, PL-44100 Gliwice, Poland

[3] Natl Univ Kyiv Mohyla Acad, Dept Math, Skovorody 2, UA-04070 Kiev, Ukraine

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 02期

关键词：

General linear Lie algebra; linear transformation; infinite-dimensional vector space; ideal;

D O I：

10.1090/proc/16162

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let V be an infinite-dimensional vector space over a field of characteristic not equal to 2. We classify ideals of the Lie algebra gl(V ) of all linear transformations of the space V.

引用

页码：467 / 473

页数：7

共 50 条

[21] Structure and representation for a class of infinite-dimensional Lie algebras
Lian, Haifeng
Tan, Shaobin
[J]. JOURNAL OF ALGEBRA, 2007, 307 (02) : 804 - 828
[22] Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras
Accardi, Luigi
Boukas, Andreas
[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2009, 5
[23] The dual coalgebra of certain infinite-dimensional Lie algebras
Griffing, G
[J]. COMMUNICATIONS IN ALGEBRA, 2002, 30 (12) : 5715 - 5724
[24] ON THE HARISHCHANDRA HOMOMORPHISM FOR INFINITE-DIMENSIONAL LIE-ALGEBRAS
CHARI, V
ILANGOVAN, S
[J]. JOURNAL OF ALGEBRA, 1984, 90 (02) : 476 - 490
[25] DEFORMATIONS OF SOME INFINITE-DIMENSIONAL LIE-ALGEBRAS
FIALOWSKI, A
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1990, 31 (06) : 1340 - 1343
[26] LEVI FACTORS OF INFINITE-DIMENSIONAL LIE-ALGEBRAS
STEWART, I
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1972, 5 (OCT): : 488 - &
[27] Infinite-dimensional (dg) Lie algebras and factorization algebras in algebraic geometry
Mikhail Kapranov
[J]. Japanese Journal of Mathematics, 2021, 16 : 49 - 80
[28] Infinite-dimensional (dg) Lie algebras and factorization algebras in algebraic geometry
Kapranov, Mikhail
[J]. JAPANESE JOURNAL OF MATHEMATICS, 2021, 16 (01): : 49 - 80
[29] INFINITE-DIMENSIONAL ALGEBRAS AND A TRIGONOMETRIC BASIS FOR THE CLASSICAL LIE-ALGEBRAS
FAIRLIE, DB
FLETCHER, P
ZACHOS, CK
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1990, 31 (05) : 1088 - 1094
[30] A Poisson basis theorem for symmetric algebras of infinite-dimensional Lie algebras
Sanchez, Omar Leon
Sierra, Susan J.
[J]. ARKIV FOR MATEMATIK, 2023, 61 (02): : 375 - 412

← 1 2 3 4 5 →