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.

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"

References in corpus (6)

• Spectral extension of the quantum group cotangent bundle
• Weyl approach to representation theory of reflection equation algebra
• Quantum line bundles on noncommutative sphere
• On The Poincare Series of Quadratic Algebras Associated to Hecke Symmetries
• Generic super-orbits in gl(m|n)* and their braided counterparts
• Braided affine geometry and q-analogs of wave operators

Cited by in corpus (7)

• Braided Weyl algebras and differential calculus on U(u(2))
• Doubles of associative algebras and their applications
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications
• q-Casimir and q-cut-and-join operators related to Reflection Equation Algebras
• Braided algebras and their applications to Noncommutative Geometry
• Noncommutative Geometry and dynamical models on U(u(2)) background
• Quantum doubles of Fock type and bosonization