Connes-Landi spheres are homogeneous spaces

• Wilson, Mitsuru ^[1]
  1. [1] Instytut Matematyczny
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 53, Nº. Extra 1, 2019 (Ejemplar dedicado a: Suplemento), págs. 257-271
• Idioma: inglés
• DOI: 10.15446/recolma.v53nsupl.84099
• Enlaces
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• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • Alain Connes, Noncommutative geometry, Academic Press, 1995.
  • Alain Connes and Michael Dubois-Violette, Noncommutative finite-dimensional manifolds. i. spherical manifolds and related examples, Communications...
  • Alain Connes and Giovanni Landi, Noncommutative manifolds: the instanton algebra and isospectral deformations, Communications in Mathematical...
  • Chiara Pagani Giovanni Landi and Cesare Reina., A hopf bundle over a quantum four-sphere from the symplectic group, Communications in Mathematical...
  • Giovanni Landi and Walter van Suijlekom, Principal fibrations from noncommutative spheres, Communications in Mathematical Physics 260 (2005),...
  • Marc Rieffel, Deformation quantization for actions of rd, Memoirs of the American Mathematical Society 506 (1993), x+93 pp.
  • Marc Rieffel, Non-commutative tori - a case study of non-commutative differentiable manifolds, Contemporary Mathematics 145 (1993), 465-491.
  • Andrzj Sitarz, Rieffel's deformation quantization and isospectral deformations, International Journal of Theoretical Physics 40 (2001),...
  • Joseph Várilly, Quantum symmetry groups of noncommutative spheres, Communications in Mathematical Physics 221 (2001), no. 3, 511-523.
  • Shuzhou Wang, Deformations of compact quantum groups via rieffel's quantization, Communications in Mathematical Physics 178 (1996), no....
  • Mitsuru Wilson, Quantum symmetries of the deformation quantization of compact lie groups, Submitted to Letters in Mathematical Physics (2019).
  • Stanislaw. Woronowicz, Compact matrix pseudogroups, Communication in Mathematical Physics 111 (1987), no. 1, 613-665.