Far East Journal of Dynamical Systems
Volume 6, Issue 1, Pages 13 - 23
(June 2004)
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COVARIANCE
ALGEBRAS OF
B. Tabatabaie Shourijeh (Iran)
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Abstract:
Let A be a -algebra and let G be a locally compact group of automorphisms of A (G acts on A as an automorphism group). Then one constructs a new -algebra which is called the -crossed product (or the covariance algebra) of the -dynamical system In this paper, first we consider the reduced crossed product, of a -dynamical system where G is a discrete group (discrete crossed product); and as a special case of that, the reduced group -algebra, is obtained. Also, it is shown that is the -algebra generated by where l is the left regular representation of G. Finally, crossed product in continuous case is explained. Also, we try to clarify the above concepts by some examples. At the end, the concept of partial crossed product of a
-algebra is introduced. |
| Keywords and phrases: unitary representation, non-degenerate representation, faithful representation, universal representation, Haar measure, modular function, orthonormal basis, C*-algebra. |
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