Derivations and 2-Cocycles of Contact Lie Algebras Related to Locally-Finite Derivations

Details Derivations and 2-Cocycles of Contact Lie Algebras Related to Locally-Finite Derivations Derivations and 2-Cocycles of Contact Lie Algebras Related to Locally-Finite Derivations

2005-11-22

arxiv.org/abs/math/0511553v1

Comm. Alg. 32 (2004), 4613-4631

Mathematics

Quantum Algebra

LaTeX, 15 pages

Scientific paper

Classical contact Lie algebras are the fundamental algebraic structures on the manifolds of contact elements of configuration spaces in classical mechanics. Xu introduced a large category of contact simple Lie algebras which are related to locally finite derivations and are in general not finitely graded. The isomorphism classes of these Lie algebras were determined in a previous paper by Xu and Su. In this paper, the derivation algebras and the 2-cohomology groups of these Lie algebras are determined, and it is obtained that the 2-cohomology groups of these Lie algebras are all trivial.

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