465 research outputs found
Lie antialgebras: premices
The main purpose of this work is to develop the basic notions of the Lie
theory for commutative algebras. We introduce a class of \mathbbZ_2-graded
commutative but not associative algebras that we call ``Lie antialgebras''.
These algebras are closely related to Lie (super)algebras and, in some sense,
link together commutative and Lie algebras. The main notions we define in this
paper are: representations of Lie antialgebras, an analog of the Lie-Poisson
bivector (which is not Poisson) and central extensions. We also classify simple
finite-dimensional Lie antialgebras.Comment: This is the final versio
Vector fields in the presence of a contact structure
We consider the Lie algebra of all vector fields on a contact manifold as a
module over the Lie subalgebra of contact vector fields. This module is split
into a direct sum of two submodules: the contact algebra itself and the space
of tangent vector fields. We study the geometric nature of these two modules.Comment: 10 page
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