Inglês (pdf)
Artigo em XML
Referências do artigo
Tradução automática
Enviar este artigo por email
Permalink
Text complete and PDF
Serviços Personalizados
Journal
Artigo
Indicadores
-
Citado por SciELO -
Acessos
Links relacionados
-
Citado por Google -
Similares em
SciELO -
Similares em Google
Compartilhar
Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.53 supl.1 Bogotá dez. 2019 Epub 24-Mar-2020
https://doi.org/10.15446/recolma.v53nsupl.84099
Artículos originales
Connes-Landi spheres are homogeneous spaces
1 Instytut Matematyczny, Polonia
In this paper, we review some recent developments of compact quantum groups that arise as θ-deformations of compact Lie groups of rank at least two. A θ-deformation is merely a 2-cocycle deformation using an action of a torus of dimension higher than 2. Using the formula (Lemma 5.3) developed in [11], we derive the noncommutative 7-sphere in the sense of Connes and Landi [3] as the fixed-point subalgebra.
Keywords: Noncommutative geometry; quantum homogeneous space; compact quantum group; Connes-Landi deformation; θ-deformation
En este artículo nosotros revisamos algunos desarrollos recientes de grupos cuánticos compactos que surgen en θ-deformaciones de grupos compactos de Lie de rango al menos dos. Una θ-deformación es simplemente una deformación por 2-cociclo, usando una acción de un toro de dimensión superior a 2. Usando la fórmula (Lemma 5.3) desarrollada en [11], nosotros derivamos la 7-esfera no conmutativa, en el sentido de Connes y Landi [3], como la subálgebra de puntos fijos.
Palabras clave: Geometría no conmutativa; espacio cuántico homogéneo; grupo cuántico compacto; deformación de Connes-Landi; θ-deformación
Acknowledgment
I would like to gratefully thank the organizers for organizing XXII Coloquio Latinoamericano de Álgebra, 2017 at Pontificial Universidad católica del Ecuador where I was able to advance my work. I would like to thank Sylvie Paycha for some fruitful discussions at this conference
References
[1] Alain Connes, Noncommutative geometry, Academic Press, 1995. [ Links ]
[2] Alain Connes and Michael Dubois-Violette, Noncommutative finite-dimensional manifolds. i. spherical manifolds and related examples, Communications in Mathematical Physics 230 (2002), no. 3, 539-579. [ Links ]
[3] Alain Connes and Giovanni Landi, Noncommutative manifolds: the instanton algebra and isospectral deformations, Communications in Mathematical Physics 221 (2001), no. 1, 141-159. [ Links ]
[4] Chiara Pagani Giovanni Landi and Cesare Reina., A hopf bundle over a quantum four-sphere from the symplectic group, Communications in Mathematical Physics 263 (2006), no. 1, 65-88. [ Links ]
[5] Giovanni Landi and Walter van Suijlekom, Principal fibrations from noncommutative spheres, Communications in Mathematical Physics 260 (2005), no. 1, 203-225. [ Links ]
[6] Marc Rieffel, Deformation quantization for actions of r d, Memoirs of the American Mathematical Society 506 (1993), x+93 pp. [ Links ]
[7]______, Non-commutative tori - a case study of non-commutative differentiable manifolds, Contemporary Mathematics 145 (1993), 465491 [ Links ]
[8] Andrzj Sitarz, Rieffel's deformation quantization and isospectral deformations, International Journal of Theoretical Physics 40 (2001), no. 10, 1693-1696. [ Links ]
[9] Joseph Várilly, Quantum symmetry groups of noncommutative spheres, Communications in Mathematical Physics 221 (2001), no. 3, 511-523. [ Links ]
[10] Shuzhou Wang, Deformations of compact quantum groups via rieffel's quantization, Communications in Mathematical Physics 178 (1996), no. 1, 747-764. [ Links ]
[11] Mitsuru Wilson, Quantum symmetries of the deformation quantization of compact lie groups, Submitted to Letters in Mathematical Physics (2019). [ Links ]
[12] Stanislaw. Woronowicz, Compact matrix pseudogroups, Communication in Mathematical Physics 111 (1987), no. 1, 613-665. [ Links ]
Received: August 11, 2018; Accepted: November 02, 2018
Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons BY
