NILPOTENT ORBITS IN THE WITT ALGEBRA W1

被引：12

作者：

Yao, Yu-Feng ^{[1
]}

Shu, Bin ^{[2
]}

机构：

[1] Shanghai Maritime Univ, Dept Math, Shanghai 201306, Peoples R China

[2] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2011年 / 39卷 / 09期

关键词：

Automorphism group; Nilpotent cone; Nilpotent orbit; The Witt algebra; SIMPLE LIE-ALGEBRAS; REPRESENTATION-THEORY; CLASSIFICATION;

D O I：

10.1080/00927872.2010.501772

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, the nilpotent orbits of the Witt algebra W-1 are determined under the automorphism group over an algebraically closed field F of characteristic p > 3. In contrast with a finite number of nilpotent orbits in a classical simple Lie algebra (cf. [5]), there is an infinite number of nilpotent orbits in W-1. A set of representatives of nilpotent orbits, as well as their dimensions, are precisely presented.

引用

页码：3232 / 3241

页数：10

共 12 条

[1] CLASSIFICATION OF THE RESTRICTED SIMPLE LIE-ALGEBRAS [J].

BLOCK, RE ;

WILSON, RL .

JOURNAL OF ALGEBRA, 1988, 114 (01) :115-259

[2]

Chang H., 1941, Abh. Math. Sem. Hansischen Univ., V14, P151

[3] Representation theory of the Witt algebra [J].

Feldvoss, J ;

Nakano, DK .

JOURNAL OF ALGEBRA, 1998, 203 (02) :447-469

[4] MODULAR REPRESENTATION-THEORY OF LIE-ALGEBRAS [J].

FRIEDLANDER, EM ;

PARSHALL, BJ .

AMERICAN JOURNAL OF MATHEMATICS, 1988, 110 (06) :1055-1093

[5]

Jantzen J. C., 2003, PROGR MATH, P1

[6]

Jantzen JC, 1998, NATO ADV SCI I C-MAT, V514, P185

[7] THE THEOREM ON RESTRICTION OF INVARIANTS, AND NILPOTENT ELEMENTS IN WN [J].

PREMET, AA .

MATHEMATICS OF THE USSR-SBORNIK, 1992, 73 (01) :135-159

[8] Simple Lie algebras of small characteristic VI. Completion of the classification [J].

Premet, Alexander ;

Strade, Helmut .

JOURNAL OF ALGEBRA, 2008, 320 (09) :3559-3604

[9]

Ree R., 1956, Trans. Amer. Math. Soc, V83, P510

[10]

Strade H., 1988, Modular Lie Algebras and their Representations

← 1 2 →