Double product integrals and Enriquez quantisation of Lie bialgebras II: The quantum Yang-Baxter equation

Details Double product integrals and Enriquez quantisation of Lie bialgebras II: The quantum Yang-Baxter equation Double product integrals and Enriquez quantisation of Lie bialgebras II: The quantum Yang-Baxter equation

2005-05-06

arxiv.org/abs/math/0505107v1

Mathematics

Quantum Algebra

Scientific paper

10.1007/s11005-005-7653-9

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.

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