Quantization of non-unitary geometric classical r-matrices
In 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-...
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paper:paper_10732780_v12_n2-3_p141_Etingof2023-06-08T16:04:55Z Quantization of non-unitary geometric classical r-matrices Graña, Matías Alejo In 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. Fil:Graña, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2005 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10732780_v12_n2-3_p141_Etingof http://hdl.handle.net/20.500.12110/paper_10732780_v12_n2-3_p141_Etingof |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
In 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. |
| author |
Graña, Matías Alejo |
| spellingShingle |
Graña, Matías Alejo Quantization of non-unitary geometric classical r-matrices |
| author_facet |
Graña, Matías Alejo |
| author_sort |
Graña, Matías Alejo |
| title |
Quantization of non-unitary geometric classical r-matrices |
| title_short |
Quantization of non-unitary geometric classical r-matrices |
| title_full |
Quantization of non-unitary geometric classical r-matrices |
| title_fullStr |
Quantization of non-unitary geometric classical r-matrices |
| title_full_unstemmed |
Quantization of non-unitary geometric classical r-matrices |
| title_sort |
quantization of non-unitary geometric classical r-matrices |
| publishDate |
2005 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10732780_v12_n2-3_p141_Etingof http://hdl.handle.net/20.500.12110/paper_10732780_v12_n2-3_p141_Etingof |
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AT granamatiasalejo quantizationofnonunitarygeometricclassicalrmatrices |
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