Covariance algebra of a partial dynamical system
- Bartosz Kosma Kwaśniewski
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A pair (X, α) is a partial dynamical system if X is a compact topological space and α: Δ→ X is a continuous mapping such that Δ is open. Additionally we assume here that Δ is closed and α(Δ) is open. Such systems arise naturally while dealing with commutative C *-dynamical systems.
In this paper we construct and investigate a universal C *-algebra C *(X,α) which agrees with the partial crossed product  in the case α is injective, and with the crossed product by a monomorphism  in the case α is onto.
The main method here is to use the description of maximal ideal space of a coefficient algebra, cf. [16, 18], in order to construct a larger system, \((\tilde X,\tilde \alpha )\) where \(\tilde \alpha \) is a partial homeomorphism. Hence one may apply in extenso the partial crossed product theory [10, 13], In particular, one generalizes the notions of topological freeness and invariance of a set, which are being use afterwards to obtain the Isomorphism Theorem and the complete description of ideals of C *(X, α).
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- Covariance algebra of a partial dynamical system
Central European Journal of Mathematics
Volume 3, Issue 4 , pp 718-765
- Cover Date
- Print ISSN
- Online ISSN
- Central European Science Journals
- Additional Links
- Crossed product
- C *-dynamical system
- covariant reqresentation
- topological freeness
- Author Affiliations
- 1. Institute of Mathematics, University in Bialystok, u. Akademicka 2, PL-15-424, Bialystok, Poland