3 research outputs found
Simple algebras of Weyl type
Over a field of any characteristic, for a commutative associative algebra
with an identity element and for the polynomial algebra of a
commutative derivation subalgebra of , the associative and the Lie
algebras of Weyl type on the same vector space are
defined. It is proved that , as a Lie algebra (modular its center) or as
an associative algebra, is simple if and only if is -simple and
acts faithfully on . Thus a lot of simple algebras are obtained.Comment: 9 pages, Late