58,454 research outputs found
A Groupoid Approach to Discrete Inverse Semigroup Algebras
Let be a commutative ring with unit and an inverse semigroup. We show
that the semigroup algebra can be described as a convolution algebra of
functions on the universal \'etale groupoid associated to by Paterson. This
result is a simultaneous generalization of the author's earlier work on finite
inverse semigroups and Paterson's theorem for the universal -algebra. It
provides a convenient topological framework for understanding the structure of
, including the center and when it has a unit. In this theory, the role of
Gelfand duality is replaced by Stone duality.
Using this approach we are able to construct the finite dimensional
irreducible representations of an inverse semigroup over an arbitrary field as
induced representations from associated groups, generalizing the well-studied
case of an inverse semigroup with finitely many idempotents. More generally, we
describe the irreducible representations of an inverse semigroup that can
be induced from associated groups as precisely those satisfying a certain
"finiteness condition". This "finiteness condition" is satisfied, for instance,
by all representations of an inverse semigroup whose image contains a primitive
idempotent
The averaging trick and the Cerny conjecture
The results of several papers concerning the \v{C}ern\'y conjecture are
deduced as consequences of a simple idea that I call the averaging trick. This
idea is implicitly used in the literature, but no attempt was made to formalize
the proof scheme axiomatically. Instead, authors axiomatized classes of
automata to which it applies
Measurement of high p_T isolated prompt photons in lead-lead collisions at sqrt(s_NN)=2.76 TeV with the ATLAS detector at the LHC
Prompt photons are a powerful tool to study heavy ion collisions. Their
production rates provide access to the initial state parton distribution
functions and also provide a means to calibrate the expected energy of jets
that are produced in the medium. The ATLAS detector measures photons with its
hermetic, longitudinally segmented calorimeter, which gives excellent spatial
and energy resolutions, and detailed information about the shower shape of each
measured photon. This provides significant rejection against the expected
background from the decays of neutral pions in jets. Rejection against jet
fragmentation products is further enhanced by requiring candidate photons to be
isolated. First results on the spectra of isolated prompt photons from a
dataset with an integrated luminosity of approximately 0.13 nb^-1 of lead-lead
collisions at sqrt(s_NN)=2.76 TeV are shown as a function of transverse
momentum and centrality. The measured spectra are compared to expectations from
perturbative QCD calculations.Comment: Proceedings for Hard Probes 2012, May 27 - June 1, 2012, Cagliari,
Sardinia, Ital
Simplicity, primitivity and semiprimitivity of etale groupoid algebras with applications to inverse semigroup algebras
This paper studies simplicity, primitivity and semiprimitivity of algebras
associated to \'etale groupoids. Applications to inverse semigroup algebras are
presented. The results also recover the semiprimitivity of Leavitt path
algebras and can be used to recover the known primitivity criterion for Leavitt
path algebras.Comment: Updated after referee report and corrected misprint
Aircraft operating efficiency on the North Atlantic, a challenge for the 1980's
A number of changes are expected to occur in the near future which could have important consequences for Atlantic flight operations for the next decade. These changes are identified and their impact on aircraft operating efficiency is discussed. Possible alternatives for North Atlantic air carriers are reviewed and strategies and actions are suggested which may give a considerable impact on fuel savings for years to come
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