Quantization of non-unitary geometric classical r-matrices

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dc.creatorEtingof, P.
dc.creatorGraña, M.
dc.date2002-12-12
dc.date.accessioned2026-07-07T04:53:46Z
dc.date.available2026-07-07T04:53:46Z
dc.descriptionIn this paper we explicitly attach to a geometric classical r-matrix $r$ (not necessarily unitary), a geometric (i.e., set-theoretical) quantum R-matrix $R$, which is a quantization of $r$. To accomplish this, we use the language of bijective cocycle 7-tuples, developed by A. Soloviev in the study of set-theoretical quantum R-matrices. Namely, we define a classical version of bijective cocycle 7-tuples, and show that there is a bijection between them and geometric classical r-matrices. Then we show how any classical bijective cocycle 7-tuple can be quantized, and finally use Soloviev's construction, which turns a (quantum) bijective cocycle 7-tuple into a geometric quantum R-matrix.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0212183
dc.identifierhttp://arxiv.org/abs/math/0212183
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65980
dc.subjectQuantum Algebra
dc.subject17B37; 53D50
dc.titleQuantization of non-unitary geometric classical r-matrices
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