1,849 research outputs found
Deformations of the Lie-Poisson sphere of a compact semisimple Lie algebra
A compact semisimple Lie algebra induces a Poisson structure
on the unit sphere in . We compute the moduli space
of Poisson structures on around . This is the first explicit
computation of a Poisson moduli space in dimension greater or equal than three
around a degenerate (i.e. not symplectic) Poisson structure.Comment: 10 pages, v3: published versio
On the domain of singular traces
The question whether an operator belongs to the domain of some singular trace
is addressed, together with the dual question whether an operator does not
belong to the domain of some singular trace. We show that the answers are
positive in general, namely for any (compact, infinite rank) positive operator
A we exhibit two singular traces, the first being zero and the second being
infinite on A. However, if we assume that the singular traces are generated by
a "regular" operator, the answers change, namely such traces always vanish on
trace-class, non singularly traceable operators and are always infinite on non
trace-class, non singularly traceable operators. These results are achieved on
a general semifinite factor, and make use of a new characterization of singular
traceability (cf. math.OA/0202108).Comment: 7 pages, LaTeX. Minor corrections, to appear on the International
Journal of Mathematic
Extensions of positive definite functions on amenable groups
Let be a subset of a amenable group such that and
. The main result of the paper states that if the Cayley graph of
with respect to has a certain combinatorial property, then every positive
definite operator-valued function on can be extended to a positive definite
function on . Several known extension results are obtained as a corollary.
New applications are also presented
Thin buildings
Let X be a building of uniform thickness q+1. L^2-Betti numbers of X are
reinterpreted as von-Neumann dimensions of weighted L^2-cohomology of the
underlying Coxeter group. The dimension is measured with the help of the Hecke
algebra. The weight depends on the thickness q. The weighted cohomology makes
sense for all real positive values of q, and is computed for small q. If the
Davis complex of the Coxeter group is a manifold, a version of Poincare duality
allows to deduce that the L^2-cohomology of a building with large thickness is
concentrated in the top dimension.Comment: This is the version published by Geometry & Topology on 24 May 200
Elementary invariants for centralizers of nilpotent matrices
We construct an explicit set of algebraically independent generators for the
center of the universal enveloping algebra of the centralizer of a nilpotent
matrix in the Lie algebra gl_N(C). In particular, this gives a new proof of the
freeness of the center, a result first proved by Panyushev, Premet and Yakimova
(math.RT/0610049).Comment: 12 page
Self-adjointness and boundedness in quadratic quantization
We construct a counter example showing, for the quadratic quantization, the
identity is not necessarily true. We characterize
all operators on the one-particle algebra whose quadratic quantization are
self-adjoint operators on the quadratic Fock space. Finally, we discuss the
boundedness of the quadratic quantization.Comment: 14 page
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