Czechoslovak Journal of Physics

, Volume 47, Issue 11, pp 1115–1122

Double quantization on the coadjoint representation of sl(n)

  • J. Donin
Article

DOI: 10.1023/A:1021654016159

Cite this article as:
Donin, J. Czechoslovak Journal of Physics (1997) 47: 1115. doi:10.1023/A:1021654016159

Abstract

For \(\mathfrak{g} = sl(n)\) we construct a two parametric \(U_h (\mathfrak{g})\)-invariant family of algebras, \((S\mathfrak{g})_{t,h} \), that is a quantization of the function algebra \(S\mathfrak{g}\) on the coadjoint representation. Along the parameter t the family gives a quantization of the Lie bracket. This family induces a two parametric \(U_h (\mathfrak{g})\)-invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-Souriau bracket. Yet we construct a quantum de Rham complex on \(\mathfrak{g}*\).

Copyright information

© Institute of Physics, Academy of Sciences of Czech Republic 1997

Authors and Affiliations

  • J. Donin
    • 1
  1. 1.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael