Advertisement

Finite Classical Groups

  • Stephen Bruce Sontz
Part of the Universitext book series (UTX)

Abstract

Let G be a finite group. The only Hausdorff topology on G is the discrete topology; that is, every subset of G is open. Since any cover of G is finite, G is compact. So the Gel’fand–Naimark theory for compact, Hausdorff spaces applies to the topological space G with the discrete topology.

Keywords

Finite Group Conjugacy Class Hopf Algebra Coxeter Group Differential Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. 5.
    B. Blackadar, Operator Algebras, Springer, 2006.Google Scholar
  2. 14.
    C. Davis and E.W. Ellers, eds., The Coxeter Legacy, Reflections and Projections, Am. Math. Soc., 2006.Google Scholar
  3. 26.
    M. Ðurđevich, Geometry of quantum principal bundles III, Alg. Groups Geom. 27 (2010) 247–336.Google Scholar
  4. 36.
    L.C. Grove and C.T. Benson, Finite Reflection Groups, Springer, 1985.Google Scholar
  5. 40.
    J.E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990.Google Scholar
  6. 41.
    T.W. Hungerford, Algebra, Springer, 1974.Google Scholar
  7. 80.
    T. Timmermann, An Invitation to Quantum Groups and Duality, Euro. Math. Soc., 2008.Google Scholar
  8. 84.
    S.L. Woronowicz, Compact matrix pseudogroups, Commun. Math. Phys. 111 (1987) 613–665.zbMATHMathSciNetCrossRefGoogle Scholar
  9. 86.
    S.L. Woronowicz, Differential calculus on compact matrix pseudogroups (quantum groups), Commun. Math. Phys. 122 (1989) 125–170.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Stephen Bruce Sontz
    • 1
  1. 1.Centro de Investigación en Matemáticas, A.C.GuanajuatoMexico

Personalised recommendations