1998/04/03 by Byung-Jay Kahng, Kahng, Byung-Jay
Mathematics · #46L87 81R50 22D25 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:22D25 #msc:46L87 #msc:81R50
paper · pdf · doi:10.48550/arxiv.math/9804019
AMS LaTeX (36 pages), Revised version of previous math.OA9804019; to appear in J. Operator Theory
arxiv created 1999/10/08 · arxiv updated 2009/11/30
The dual Lie bialgebra of a certain ``quasitriangular'' Lie bialgebra structure on the Heisenberg Lie algebra determines a (non-compact) Poisson--Lie group G. The compatible Poisson bracket on G is non-linear, but it can still be realized as a ``cocycle perturbation'' of the linear Poisson bracket. We construct a certain twisted group C*-algebra A, which is shown to be a strict deformation quantization of G. Motivated by the data at the Poisson (classical) level, we then construct on A its locally compact quantum group structures: comultiplication, counit, antipode and Haar weight, as well as its associated multiplicative unitary operator. We also find a quasitriangular ``quantum universal R-matrix'' type operator for A, which agrees well with the quasitriangularity at the Lie bialgebra level.