Non-formal star-exponential on contracted one-sheeted hyperboloids
Operator Algebras
2016-02-10 v2 Mathematical Physics
math.MP
Quantum Algebra
Representation Theory
Abstract
In this paper, we exhibit the non-formal star-exponential of the Lie group SL(2,R) realized geometrically on the curvature contraction of its one-sheeted hyperboloid orbits endowed with its natural non-formal star-product. It is done by a direct resolution of the defining equation of the star-exponential and produces an expression with Bessel functions. This yields a continuous group homomorphism from SL(2,R) into the von Neumann algebra of multipliers of the Hilbert algebra underlied by this natural star-product. As an application, we prove a new identity on Bessel functions.
Keywords
Cite
@article{arxiv.1501.07491,
title = {Non-formal star-exponential on contracted one-sheeted hyperboloids},
author = {Pierre Bieliavsky and Axel de Goursac and Yoshiaki Maeda and Florian Spinnler},
journal= {arXiv preprint arXiv:1501.07491},
year = {2016}
}
Comments
33 pages, 3 figures, v2: changes in section 3, references added