Artículo
Etingof, P.; Graña, M. "Quantization of non-unitary geometric classical r-matrices" (2005) Mathematical Research Letters. 12(2-3):141-153
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | Quantization of non-unitary geometric classical r-matrices |
| Autor: | Etingof, P.; Graña, M. |
| Filiación: | MIT Math. Dept. of. 2-176, 77 Mass. Ave., Cambridge, MA 02139, United States MIT Math. Dept. of. 2-155, 77 Mass. Ave., Cambridge, MA 02139, United States Depto. Matemática, FCEyN, Ciudad Universitaria, (1428) Ciudad de Buenos Aires, Argentina |
| Año: | 2005 |
| Volumen: | 12 |
| Número: | 2-3 |
| Página de inicio: | 141 |
| Página de fin: | 153 |
| DOI: | http://dx.doi.org/10.4310/MRL.2005.v12.n2.a1 |
| Título revista: | Mathematical Research Letters |
| Título revista abreviado: | Math. Res. Lett. |
| ISSN: | 10732780 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10732780_v12_n2-3_p141_Etingof |
Referencias:
- Drinfeld, V., Some unsolved problems in quantum group theory (1990) Quantum Groups, pp. 1-8. , [D] (Leningrad)
- (1992) Lecture Notes in Math., 1510. , Springer, Berlin
- Etingof, P., Kazhdan, D., Quantization of Lie bialgebras. I (1996) Selecta Math. (N.S.), 2, pp. 1-41. , [EK]
- Etingof, P., Soloviev, A., Quantization of geometric classical r-matrices (1999) Math. Res. Lett., 6, pp. 223-228. , [ES]
- Etingof, P., Schedler, T., Soloviev, A., Set-theoretical solutions to the quantum Yang-Baxter equation (1999) Duke Math. J., 100, pp. 169-209. , [ESS]
- Fenn, R., Rourke, C., Racks and links in codimension two (1992) J. Knot Theory Ramifications, 1, pp. 343-406. , [FR]
- Soloviev, A., Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation (2000) Math. Res. Lett., 7, pp. 577-596. , [S]
Citas:
---------- APA ----------
Etingof, P. & Graña, M. (2005) . Quantization of non-unitary geometric classical r-matrices. Mathematical Research Letters, 12(2-3), 141-153.http://dx.doi.org/10.4310/MRL.2005.v12.n2.a1
---------- CHICAGO ----------
Etingof, P., Graña, M. "Quantization of non-unitary geometric classical r-matrices" . Mathematical Research Letters 12, no. 2-3 (2005) : 141-153.http://dx.doi.org/10.4310/MRL.2005.v12.n2.a1
---------- MLA ----------
Etingof, P., Graña, M. "Quantization of non-unitary geometric classical r-matrices" . Mathematical Research Letters, vol. 12, no. 2-3, 2005, pp. 141-153.http://dx.doi.org/10.4310/MRL.2005.v12.n2.a1
---------- VANCOUVER ----------
Etingof, P., Graña, M. Quantization of non-unitary geometric classical r-matrices. Math. Res. Lett. 2005;12(2-3):141-153.http://dx.doi.org/10.4310/MRL.2005.v12.n2.a1
