$H_D$-Quantum Vertex Algebras and Bicharacters

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dc.creatorAnguelova, Iana I.
dc.creatorBergvelt, Maarten J.
dc.date2007-06-11
dc.date.accessioned2026-07-07T08:04:57Z
dc.date.available2026-07-07T08:04:57Z
dc.descriptionWe define a new class of quantum vertex algebras, based on the Hopf algebra $H_D=\mathbb{C}[D]$ of "infinitesimal translations" generated by $D$. Besides the braiding map describing the obstruction to commutativity of products of vertex operators, $H_D$-quantum vertex algebras have as main new ingredient a "translation map" that describes the obstruction of vertex operators to satisfying translation covariance. The translation map also appears as obstruction to the state-field correspondence being a homomorphism. We use a bicharacter construction of Borcherds to construct a large class of $H_D$-quantum vertex algebras. One particular example of this construction yields a quantum vertex algebra that contains the quantum vertex operators introduced by Jing in the theory of Hall-Littlewood polynomials.
dc.description46 pages
dc.identifierhttps://arxiv.org/abs/0706.1528
dc.identifierhttp://arxiv.org/abs/0706.1528
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130151
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subject17B69
dc.title$H_D$-Quantum Vertex Algebras and Bicharacters
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