Braided Differential Operators on Quantum Algebras

Abstract

We define the braided differential algebras which can be interpreted as quantization of the differential operator algebra defined on some algebraic varieties supplied with the action of the group GL(m). The algebra is generated by right invariant or coajoint vector fields. Our main example is gl^*(m) and coadjoint orbits in it. The Heisenberg double on the quantum group Fun_q(GL(m)is a particular case of the suggested construction.Comment: Corrected and extended version. An illustrative example is added into the Section 5. LaTex file, 24 pp. Accepted for publication in "Journal of Geometry and Physics