Locally compact transformation groups and 𝐶*-algebras

Effros, Edward G.; Hahn, F.

doi:10.1090/s0002-9904-1967-11690-2

Cited by 137 publications

(167 citation statements)

References 9 publications

Supporting

Mentioning

163

Contrasting

Unclassified

Order By: Relevance

“…We note that when © = Y X G as in 2.6.3, then L7(©) is closely related to, but different from, an Lx -algebra which intervenes in the theory of transformation group C*-algebras [15] and, more generally, in the theory of C*-crossed products [28]. Also we mention here, although it takes a little proof, that C*( © ) coincides with the usual transformation group C*-algebra bases on (Y, G).…”

Section: ])mentioning

confidence: 95%

See 1 more Smart Citation

Untitled

1982

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. The C*-algebra 28 generated by the Wiener-Hopf operators defined over a subsemigroup of a locally compact group is shown to be the image of a groupoid C*-algebra under a suitable representation. When the subsemigroup is either a polyhedral cone or a homogeneous, self-dual cone in an Euclidean space, this representation may be used to show that 28 is postliminal and to find a composition series with very explicit subquotients. This yields a concrete parameterization of the spectrum of 28 and exhibits the topology on it.

show abstract

Section: ])mentioning

confidence: 95%

“…Thus, except for the missing modular function, we see that J implements a unitary equivalence between Ind (i and the usual representation of C*(@) which is induced by the representation of C0(Y) as multiplication operators on L2(ii) (cf. [15,26]). This explains the terminology and notation.…”

Section: ])mentioning

confidence: 99%

Untitled

1982

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…In this paper we begin the investigation of a very general class of algebras of functions on locally compact groups taking values in a Banach algebra. A number of authors have investigated special cases of such algebras, notably G. P. Johnson [12], J. Glimm [8], E. Effros and F. Hahn [6], Turumaru [23], Zeller-Meier [26], I. Segal [20], and Doplicher, Kastler and Robinson [5]. Of these, Zeller-Meier's algebras come closest in generality to those we discuss.…”

mentioning

confidence: 88%

“…Example 2 was studied by G. P. Johnson in [12]. The álgebras of Example 3 have been considered from a rather different point of view, attention being restricted to the enveloping C*-algebras, by Glimm [8] and by Effros and Hahn [6].…”

Section: Let G Be a Locally Compact Group With Left Haar Measure Dg Amentioning

confidence: 99%

See 1 more Smart Citation

Representations of twisted group algebras

Busby¹,

Smith²

1970

Trans. Amer. Math. Soc.

113

167

View full text Add to dashboard Cite

Abstract. We construct a general class of Banach algebras which include as special cases the group algebra of a locally compact group, the group algebra of a group extension (in terms of the subgroup and quotient group), and some other examples, special cases of which have been studied under the name of covariance algebras. We develop the general representation theory and generalize Mackey's theory of induced representations.

show abstract

Ideals in Some Continuous Nonselfadjoint Crossed Product Algebras

Lamoureux

1996

Journal of Functional Analysis

View full text Add to dashboard Cite

Let (Y, , t ) be a locally compact dynamical system, where the , t denotes a continuous, one parameter semigroup of maps on Y. When each , t is a homeomorphism, a nonselfadjoint crossed product algebra is defined as the subalgebra of the C*-crossed product C 0 (Y ) < R supported on t>0; when each , t is only continuous, the crossed product C 0 (Y ) < R + can still be defined. The ideal structure of such an algebra is determined in the case where the semigroup action is the suspension of a discrete, free action on a smaller space X. A generalization of Effros Hahn is given, whereby one may find a meet-irreducible ideal over any arc closure in Y. The meet-irreducible ideals form a topological space in the hullkernel topology, and there is a one-to-one correspondence between closed sets in this space and closed ideals in the algebra. A subset of this space is homeomorphic to the space of finite arcs in the subarc topology. The irrational flow algebra is considered as a special case.

show abstract

Locally compact transformation groups and 𝐶*-algebras

Cited by 137 publications

References 9 publications

Untitled

Untitled

Representations of twisted group algebras

Ideals in Some Continuous Nonselfadjoint Crossed Product Algebras

Contact Info

Product

Resources

About