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Proceedings of the American Mathematical Society

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

 
 

 

Group $C^ *$-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
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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 $\mathfrak {g}$.


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Keywords: Compact domain, group <IMG WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^*}$">-algebra, Lie algebra of a Lie group, continuous operator function
Article copyright: © Copyright 1989 American Mathematical Society