摘要
Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A?F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras.
Over a field F of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector space A［D]=A［D] from any pair of a commutative associative algebra A with an identity element and the polynomial algebra ［D] of a commutative derivation subalgebra D of A. We prove that A[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only if A is D－simple and A［D] acts faithfully on A. Thus we obtain a lot of simple algebras.
基金
This work was supported by the National Natural Science Foundation of China (Grant No. 19801037)
a Fund from National Education Ministry of China.
