On central elements in the universal enveloping algebras of the orthogonal Lie algebras

被引：28

作者：

Itoh, M ^{[1
]}

Umeda, T ^{[1
]}

机构：

[1] Kyoto Univ, Fac Sci, Dept Math, Kyoto 606, Japan

来源：

COMPOSITIO MATHEMATICA | 2001年 / 127卷 / 03期

关键词：

center of universal enveloping algebra; orthogonal Lie algebra;

D O I：

10.1023/A:1017571403369

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present an analogy of the famous formula that the square of the Pfaffian is equal to the determinant for an alternating matrix for the case where the entries are the generators of the orthogonal Lie algebras. This identity clarifies the relation between the two sets of central elements in the enveloping algebra of the orthogonal Lie algebras. We employ systematically the exterior calculus for the proof.

引用

页码：333 / 359

页数：27

共 20 条

[1]

Capelli A., 1890, MATH ANN, V37, P1

[2]

Capelli A., 1887, MATH ANN, V29, P331

[3]

Gelfand, 1950, MAT SBORNIK, V26, P103

[4] CORRECTION [J].