On algebraic curves for commuting elements in q-Heisenberg algebras

Cherednik Algebras for Algebraic Curves

For any algebraic curve C and n ≥ 1, P. Etingof introduced a ‘global’ Cherednik algebra as a natural deformation of the cross product D(Cn)⋊Sn, of the algebra of differential operators on Cn and the symmetric group. We provide a construction of the global Cherednik algebra in terms of quantum Hamiltonian reduction. We study a category of character Dmodules on a representation scheme associated ...

A note on centralizers in q-deformed Heisenberg algebras

We reprove and generalize several results (including the main one) from the recent monograph [3] using the technique of generalized Weyl algebras.

Vertex Algebras and Algebraic Curves

Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

q-Deforming Maps for Lie Group Covariant Heisenberg Algebras

We briefly summarize our systematic construction procedure of qdeforming maps for Lie group covariant Weyl or Clifford algebras. Talk presented at the Fifth Wigner Symposium, 25-29 August 1997, Vienna, Germany. Submitted for the proceedings of the Conference.