Open orbits and primitive zero ideals for solvable Lie algebras

被引：2

作者：

Baklouti, Ali ^{[2
]}

Ishi, Hideyuki ^{[1
]}

机构：

[1] Osaka Metropolitan Univ, Dept Math, 3-3-138 Sugimoto,Sumiyoshi ku, Osaka 5588585, Japan

[2] Univ Sfax, Fac Sci Sfax, Dept Math, Route Soukra,BP 1171, Sfax 3038, Tunisia

来源：

FORUM MATHEMATICUM | 2024年 / 36卷 / 03期

关键词：

Solvable Lie algebra; Frobenius Lie algebra; irreducible unitary representation; coadjoint orbit; primitive ideal;

D O I：

10.1515/forum-2022-0307

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of the paper is to provide a characterization criterion of exponential solvable Frobenius Lie algebras (having open coadjoint orbits), in terms of primitive ideals of the associated enveloping algebra. In the case of complex solvable Lie algebras, we also show that an algebraic adjoint orbit is open if and only if the associated primitive ideal through the Dixmier map is trivial.

引用

页码：571 / 584

页数：14

共 15 条

[1]

Baklouti A, 2021, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-3-030-82044-2

[2] Co-adjoint orbits and characteristic varieties [J].

Baklouti, A ;

Dhieb, S ;

Manchon, D .

JOURNAL OF GEOMETRY AND PHYSICS, 2005, 54 (01) :1-41

[3]

Baklouti A., 2019, SPINGER P MATH STAT, V290, P207

[4]

Baklouti A., 2022, GRUYTER EXP MATH, V72

[5]

BERNAT P, 1972, REPRESENTATIONS GROU

[6]

DIXMIER J, 1966, J MATH PURE APPL, V45, P1

[7]

Kurniadi E., 2019, SPRINGER P MATH STAT, V290, P95

[8]

Leptin H., 1994, Unitary Representation Theory of Exponential Lie groups

[9]

MOSCOVICI H, 1978, ANN I H POINCARE A, V29, P139

[10]

Moscovici H., 1976, REV ROUMAINE MATH PU, V21, P529

← 1 2 →