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Proceedings of the American Mathematical Society

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Group $ C\sp *$-algebras as algebras of ``continuous functions'' with noncommuting variables

Author: Wojciech Szymański
Journal: Proc. Amer. Math. Soc. 107 (1989), 353-359
MSC: Primary 46L05; Secondary 22D25
MathSciNet review: 975659
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Abstract: It is shown that a system of commutation relations depending on the structure constants of a Lie algebra $ \mathfrak{g}$ leads to a $ {C^*}$-algebra which is isomorphic to the group $ {C^*}$-algebra of the simply connected Lie group associated with $ \mathfrak{g}$.

References [Enhancements On Off] (What's this?)

  • [1] P. Kruszynski and S. L. Woronowicz, A noncommutative Gelfand-Naimark theorem, J. Operator Theory 8 (1982), 361-389. MR 677419 (84b:46068)
  • [2] E. Nelson, Analytic vectors, Ann. of Math. 70 (1959), 572-615. MR 0107176 (21:5901)
  • [3] E. Nelson and W. F. Stinespring, Representation of elliptic operators in an enveloping algebra, Amer. J. Math. 81 (1959), 547-560. MR 0110024 (22:907)
  • [4] G.K. Pedersen, $ {C^*}$-algebras and their automorphism groups, Academic Press, London-New York-San Francisco, 1979. MR 548006 (81e:46037)
  • [5] G. Warner, Harmonic analysis on semi-simple Lie group, vol. I, Springer-Verlag, Berlin-Heidelberg-New York, 1972.

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Keywords: Compact domain, group $ {C^*}$-algebra, Lie algebra of a Lie group, continuous operator function
Article copyright: © Copyright 1989 American Mathematical Society

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