数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 814-828.doi: 10.1016/S0252-9602(14)60052-7

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GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS

陈正新   

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
  • 收稿日期:2013-04-23 修回日期:2013-07-16 出版日期:2014-05-20 发布日期:2014-05-20
  • 基金资助:

    The author is supported by the National Natural Sci-ence Foundation of China (11101084, 11071040) and the Fujian Province Nature Science Foundation of China (2013J01005).

GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS

CHEN Zheng-Xin   

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
  • Received:2013-04-23 Revised:2013-07-16 Online:2014-05-20 Published:2014-05-20
  • Supported by:

    The author is supported by the National Natural Sci-ence Foundation of China (11101084, 11071040) and the Fujian Province Nature Science Foundation of China (2013J01005).

摘要:

Let P be a parabolic subalgebra of a general linear Lie algebra gl(n, F) over a field F, where n ≥ 3, F contains at least n different elements, and char(F) ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.

关键词: Parabolic subalgebras, general linear Lie algebras, generalized derivations, quasiderivations, product zero derivations

Abstract:

Let P be a parabolic subalgebra of a general linear Lie algebra gl(n, F) over a field F, where n ≥ 3, F contains at least n different elements, and char(F) ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.

Key words: Parabolic subalgebras, general linear Lie algebras, generalized derivations, quasiderivations, product zero derivations

中图分类号: 

  • 17B40