Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1989-0975659-6
MathSciNet review: 975659
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05, 22D25

Retrieve articles in all journals with MSC: 46L05, 22D25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0975659-6
Keywords: Compact domain, group $ {C^*}$-algebra, Lie algebra of a Lie group, continuous operator function
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society