Crossed Products With Continuous Trace by Siegfried Echterhoff

By Siegfried Echterhoff

The significance of separable non-stop hint $C^*$-algebras arises from the next evidence: first of all, their strong isomorphism periods are thoroughly classifiable via topological information and, secondly, continuous-trace $C^*$-algebras shape the construction blocks of the extra normal style I $C^*$-algebras. This memoir offers an in depth examine of strongly non-stop activities of abelian in the community compact teams on $C^*$-algebras with non-stop hint. less than a few common assumptions at the underlying procedure $(A,G,\alpha )$, precious and adequate stipulations are given for the crossed product $A{\times }_{\alpha }G$ to have non-stop hint, and a few kinfolk among the topological information of $A$ and $A{\times }_{\alpha }G$ are got. the consequences are utilized to enquire the constitution of staff $C^*$-algebras of a few two-step nilpotent teams and solvable Lie teams.

For readers' comfort, expositions of the Mackey-Green-Rieffel desktop of triggered representations and the speculation of Morita an identical $C^*$-dynamical platforms are integrated. there's additionally an in depth elaboration of the illustration thought of crossed items via activities of abelian teams on style I $C^*$-algebras, leading to a brand new description of activities resulting in variety I crossed items.

Features:

The newest effects at the conception of crossed items with non-stop hint.

Applications to the illustration conception of in the community compact teams and constitution of team $C^*$-algebras.

An exposition at the sleek idea of precipitated representations.

New effects on kind I crossed items.

Show description

Read or Download Crossed Products With Continuous Trace PDF

Best products books

PIC Microcontrollers: Know It All (Newnes Know It All)

Whereas the cloth within the ebook is reasonable, i feel the authors and writer have been simply attempting to make an enormous publication with loads of pages. A unfastened Newnes on-line club is marketed at the disguise that is presupposed to provide you with "four loose downloadable choices from best specialists at the slicing edge", yet there is not any details on the way to make the most of this supply and emails to [.

Motion Control in Offshore and Dredging

Movement keep watch over unearths purposes in lots of offshore, subsea and dredging installations. movement keep an eye on is often according to a mix of mechanical-, electric- and hydraulic force structures including keep an eye on innovations. The ebook presents the elemental thought of hydraulic controls, behaviour of hydraulic fluids, hydraulic part capabilities, parameter decisions, calculation of simple hydraulic structures and simple thought of electric drives: asynchronous automobiles with frequency drives.

Food preservation process design

The upkeep tactics for meals have developed over numerous centuries, yet fresh cognizance to non-thermal applied sciences means that a brand new size of switch has been initiated. the recent size to be emphasised is the rising applied sciences for protection of meals and the necessity for sound base of knowledge to be built as inputs for systematic strategy layout.

Additional info for Crossed Products With Continuous Trace

Sample text

Z^^a. 4. 10. i&R extends to a *-homomorphism from G 0 (O,A) onto A which is G-equivariant with respect to the diagonal action of G on Co (ft, A). ) = potyR is equal to the pair (R(p),p) G O x A = LEMMA c0(n,Ar. Suppose now that (A, G, a, r) is a twisted covariant system and that H is a closed subgroup of G such that there exists a continuous G-equivariant map R from Prim(j4) onto G/H. Then it is easily seen that *&R transports f onto r . Thus, $R implements a canonical surjective *-homomorphism, say \£, from BT = C0(G/H, A) x ^ f G onto A x a >T G.

CCR) if and only if the G-orbit G(W) is locally closed (resp. closed) in Hy for all W G 71. If this is true, then ind^ v W is irreducible for all W G 71, and induction defines a bijection between the G-orbits in 7Z and G. A locally compact group G is called monomial if every irreducible representation of G is induced from a one-dimensional representation of some subgroup. Recall also that a group G is called metabelian (or two-step solvable) if the commutator subgroup [G, G] of G is abelian. 4.

Thus {TT X U} is a Ginvariant locally closed subset of Prim(A xa G). Let B denote the corresponding subquotient of A xa G. Then B x^G is a locally closed subset of (A xa G) x^G. 2). To this end suppose that p' is an element of A such that 46 3. REPRESENTATIONS OF T Y P E I ABELIAN T W I S T E D SYSTEMS INDp' G (B x^Gy. 2 that ker(7r xU) = ker (resf lc} (INDp')) = ker(indf e} p'), from which follows that p' is in the quasi-orbit of p. 13, Prim(f? x ^ G) consists of only one G-orbit with respect to the double dual action a, we conclude that the orbit of ker p' in Prim(A) is locally closed.

Download PDF sample

Rated 4.57 of 5 – based on 14 votes