387 research outputs found
A remark on the rank conjecture
We prove a result about the action of -operations on the homology of linear groups. We use this to give a sharper formulation of the rank conjecture as well as some shorter proofs of various known results. We formulate a conjecture about how the sharper formulation of the rank conjecture together with another conjecture could give rise to a different point of view on the isomorphism between and K_n^{(p)} (F)$ for an infinite field F, and we prove part of this new conjecture
Amenable crossed product Banach algebras associated with a class of -dynamical systems
We prove that the crossed product Banach algebra that is
associated with a -dynamical system is amenable
if is a discrete amenable group and is a commutative or finite
dimensional -algebra. Perspectives for further developments
are indicated.Comment: Improved discussion of the relation with the existing literature and
of perspectives for further developments. 8 pages. To appear in Integral
Equations and Operator Theor
The structure of doubly non-commuting isometries
Suppose that and that, for all and with
and , are given such that
for all . If are
isometries on a Hilbert space such that for
all , then is called an -tuple of doubly
non-commuting isometries. The generators of non-commutative tori are well-known
examples. In this paper, we establish a simultaneous Wold decomposition for
. This decomposition enables us to classify such -tuples
up to unitary equivalence. We show that the joint listing of a unitary
equivalence class of a representation of each of the non-commutative tori
that are naturally associated with the structure constants is a classifying
invariant. A dilation theorem is also established, showing that an -tuple of
doubly non-commuting isometries can be extended to an -tuple of doubly
non-commuting unitary operators on an enveloping Hilbert space.Comment: A remark on the relation between the dilation theorem in this paper
and other dilation theorems for multiple operators in the literature has been
added. Otherwise, there are only a few minor editorial changes compared to
the first version; some typos have also been corrected. Final version, to
appear in Advances in Mathematic
Nonsimplicity of certain universal C^*-algebras
Given nā„2" role="presentation">nā„2, zijāT" role="presentation">zijāT such that zij=zĀÆji" role="presentation">zij=zĀÆji for 1ā¤i,jā¤n" role="presentation">1ā¤i,jā¤n and zii=1" role="presentation">zii=1 for 1ā¤iā¤n" role="presentation">1ā¤iā¤n, and integers p1,ā¦,pnā„1" role="presentation">p1,ā¦,pnā„1, we show that the universal C*" role="presentation">Cā-algebra generated by unitaries u1,ā¦,un" role="presentation">u1,ā¦,un such that uipiujpj=zijujpjuipi" role="presentation">upiiupjj=zijupjjupii for 1ā¤i,jā¤n" role="presentation">1ā¤i,jā¤n is not simple if at least one exponent pi" role="presentation">pi is at least two. We indicate how the method of proof by āworking with various quotientsā can be used to establish nonsimplicity of universal C*" role="presentation">Cā-algebras in other cases.Article / Letter to editorMathematisch Instituu
Introduction to the issue on heterogeneous data access and use for geospatial user communities - part II
The four papers in this second part of this special issue focus on heterogeneous data access and use for geospatial user communities. The first two papers relate to satellite remote sensing data and the second two are from the hydro-meteorological domain
Phase diagram and critical properties in the Polyakov--Nambu--Jona-Lasinio model
We investigate the phase diagram of the so-called
Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical
potential with three quark flavours. Chiral and deconfinement phase transitions
are discussed, and the relevant order-like parameters are analyzed. The results
are compared with simple thermodynamic expectations and lattice data. A special
attention is payed to the critical end point: as the strength of the
flavour-mixing interaction becomes weaker, the critical end point moves to low
temperatures and can even disappear.Comment: Talk given at the 9th International Conference on Quark Confinement
and the Hadron Spectrum - QCHS IX, Madrid, Spain, 30 August - September 201
Reply to comment by J. Wang and R.L. Bras on āEstimating the soil temperature profile from a single depth observation: A simple empirical heatflow solution"
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