Double product integrals and Enriquez quantisation of Lie bialgebras II: The quantum Yang-Baxter equation
Quantum Algebra
2009-11-11 v1
Abstract
For a Lie algebra with Lie bracket got by taking commutators in a nonunital associative algebra L, let T(L) be the vector space of tensors over L equipped with the Ito Hopf algebra structure derived from the associative multiplication in L. We show a necessary and sufficient condition that the double product integral satisfy the quantum Yang-Baxter equation over T(L). We construct a quantisation of an arbitrary quasitriangular Lie bialgebra structure on L in the unital associative subalgebra of T(L)[[h]] consisting of formal power series whose zero order coefficient lies in the space S(L) of symmetric tensors.
Keywords
Cite
@article{arxiv.math/0505107,
title = {Double product integrals and Enriquez quantisation of Lie bialgebras II: The quantum Yang-Baxter equation},
author = {R. L. Hudson and S. Pulmannova},
journal= {arXiv preprint arXiv:math/0505107},
year = {2009}
}