Derivation algebras and 2-cocycles of the algebras of q-differential operators

摘要

In the paper, the deriviation algebras of the associative algebras of the one-variable (resp. multivariable) q-differential operators and of their corresponding Lie algebras are determined. The completeness of the derivation algebras of the algebras of q-differential operators is also discussed. Finally, we calculate H-2 (D-q (n)(-), C) for n greater than or equal to 1, as well as H-2(gl(n) (D-q), C) under the assumption that q is transcendental over the rational numbers field Q.