Simple Algebras of Weyl Type
نویسندگان
چکیده
Over a field IF of any characteristic, for a commutative associative algebra A with an identity element and for the polynomial algebra IF [D] of a commutative derivation subalgebra D of A, the associative and the Lie algebras of Weyl type on the same vector space A[D] = A ⊗ IF [D] are defined. It is proved that A[D], as a Lie algebra (modular 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 a lot of simple algebras are obtained.
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