# Covariance algebra of a partial dynamical system

Open Mathematics (2005)

- Volume: 3, Issue: 4, page 718-765
- ISSN: 2391-5455

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topBartosz Kosma Kwaśniewski. "Covariance algebra of a partial dynamical system." Open Mathematics 3.4 (2005): 718-765. <http://eudml.org/doc/268682>.

@article{BartoszKosmaKwaśniewski2005,

abstract = {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 [10] in the case α is injective, and with the crossed product by a monomorphism [22] 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).},

author = {Bartosz Kosma Kwaśniewski},

journal = {Open Mathematics},

keywords = {47L65; 46L45; 37B99},

language = {eng},

number = {4},

pages = {718-765},

title = {Covariance algebra of a partial dynamical system},

url = {http://eudml.org/doc/268682},

volume = {3},

year = {2005},

}

TY - JOUR

AU - Bartosz Kosma Kwaśniewski

TI - Covariance algebra of a partial dynamical system

JO - Open Mathematics

PY - 2005

VL - 3

IS - 4

SP - 718

EP - 765

AB - 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 [10] in the case α is injective, and with the crossed product by a monomorphism [22] 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).

LA - eng

KW - 47L65; 46L45; 37B99

UR - http://eudml.org/doc/268682

ER -

## References

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