Derivations and automorphism groups of completed Witt Lie algebra

Details Derivations and automorphism groups of completed Witt Lie algebra Derivations and automorphism groups of completed Witt Lie algebra

2010-05-28

arxiv.org/abs/1005.5239v1

Mathematics

Rings and Algebras

11 pages

Scientific paper

In this paper, a simple Lie algebra, referred to as the completed Witt Lie algebra, is introduced. Its derivation algebra and automorphism group are completely described. As a byproduct, it is obtained that the first cohomology group of this Lie algebra with coefficients in its adjoint module is trivial. Furthermore, we completely determine the conjugate classes of this Lie algebra under its automorphism group, and also obtain that this Lie algebra does not contain any nonzero ad-locally finite element.

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