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Proceedings of the American Mathematical Society

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Isometries of noncommutative metric spaces

Author: Efton Park
Journal: Proc. Amer. Math. Soc. 123 (1995), 97-105
MSC: Primary 46L85
MathSciNet review: 1213868
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Abstract: A. Connes has shown that a unital ${C^ \ast }$-algebra equipped with an unbounded Fredholm module can be viewed as a "noncommutative" metric space. In this paper, the author defines a notion of an isometry of a noncommutative metric space, and computes several examples.

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  • A. Connes, Compact metric spaces, Fredholm modules, and hyperfiniteness, Ergodic Theory Dynam. Systems 9 (1989), no. 2, 207–220. MR 1007407, DOI
  • Alain Connes and John Lott, The metric aspect of noncommutative geometry, New symmetry principles in quantum field theory (Cargèse, 1991) NATO Adv. Sci. Inst. Ser. B Phys., vol. 295, Plenum, New York, 1992, pp. 53–93. MR 1204452
  • Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561

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Keywords: Noncommutative topology, noncommutative geometry, automorphisms of <!– MATH ${C^ \ast }$ –> <IMG WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^ \ast }$">-algebras
Article copyright: © Copyright 1995 American Mathematical Society