Defining relations for classical Lie algebras of polynomial vector fields
Abstract
We explicitly describe the defining relations for simple Lie algebra of vector fields with polynomial coefficients and its subalgebras of divergence free, hamiltonian and contact vector fields, and for the Poisson algebra (realized on polynomials). We consider generators of these Lie algebras corresponding to the systems of simple roots associated with the standard grading of these algebras. (These systems of simple roots are distinguished in the sense of Penkov and Serganova.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2005
 DOI:
 10.48550/arXiv.math/0510019
 arXiv:
 arXiv:math/0510019
 Bibcode:
 2005math.....10019L
 Keywords:

 Representation Theory;
 17B01;
 17B32
 EPrint:
 11 pages, Latex