Acta mathematica scientia, Series B >
GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS
Received date: 2013-04-23
Revised date: 2013-07-16
Online 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).
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.
CHEN Zheng-Xin . GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS[J]. Acta mathematica scientia, Series B, 2014 , 34(3) : 814 -828 . DOI: 10.1016/S0252-9602(14)60052-7
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