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

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R. L. Hudson, S. Pulmannova

Quantum Algebra · Submitted 6 May 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show a necessary and sufficient condition that the double product integral satisfy the quantum Yang-Baxter equation over T(L).

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arXiv IDmath/0505107 (version 1)
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CitationR. L. Hudson, S. Pulmannova. "Double product integrals and Enriquez quantisation of Lie bialgebras II: The quantum Yang-Baxter equation." arXiv:math/0505107 (2005). https://pith.science/paper/N53JNSMC
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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.06 · mentions code or data availability 0.02.

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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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s0 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. background 0.99 0.24 0.03 asserted 0.98
s1 We show a necessary and sufficient condition that the double product integral satisfy the quantum Yang-Baxter equation over T(L). result 0.93 0.95 0.60 asserted 1.00
s2 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. contribution 0.78 0.95 0.33 asserted 1.00

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Original 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.

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