Quantum isometry groups of noncommutative manifolds associated to group C*-algebras

JOURNAL OF GEOMETRY AND PHYSICS

卷:60

Article

Bhowmick, Jyotishman²  Skalski, Adam^1,3 

[1] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England

[2] Indian Stat Inst, Stat Math Unit, Kolkata 700208, India

[3] Univ Lodz, Fac Math & Comp Sci, PL-90238 Lodz, Poland

关键词: Group C*-algebra;    Spectral triple;    Quantum isometry group;   

DOI  :  10.1016/j.geomphys.2010.05.007

来源: Elsevier

【 摘 要 】

Let Gamma be a finitely generated discrete group. The standard spectral triple on the group C*-algebra C* (Gamma) is shown to admit the quantum group of orientation preserving isometrics. This leads to new examples of compact quantum groups In particular, the quantum isometry group of the C*-algebra of the free group on n generators is computed and turns out to be a quantum group extension of the quantum permutation group A(2n) of Wang. The quantum groups of orientation and real structure preserving isometrics are also considered and the construction of the Laplacian for the standard spectral triple on C*(Gamma) is discussed (C) 2010 Elsevier B V All rights reserved.

【 授权许可】

Free