18,953 research outputs found
Decomposition and Oxidation of the N-Extended Supersymmetric Quantum Mechanics Multiplets
We furnish an algebraic understanding of the inequivalent connectivities
(computed up to ) of the graphs associated to the irreducible
supermultiplets of the N-extended Supersymmetric Quantum Mechanics. We prove
that the inequivalent connectivities of the N=5 and N=9 irreducible
supermultiplets are due to inequivalent decompositions into two sets of N=4
(respectively, N=8) supermultiplets. "Oxido-reduction" diagrams linking the
irreducible supermultiplets of the N=5,6,7,8 supersymmetries are presented. We
briefly discuss these results and their possible applications.Comment: 15 pages, 5 figure
Refining the classification of the irreps of the 1D N-Extended Supersymmetry
The linear finite irreducible representations of the algebra of the 1D
-Extended Supersymmetric Quantum Mechanics are discussed in terms of their
"connectivity" (a symbol encoding information on the graphs associated to the
irreps). The classification of the irreducible representations with the same
fields content and different connectivity is presented up to .Comment: Two extra cases added. Reply to hep-th/0611060v2 comments adde
A duality of locally compact groups which does not involve the Haar measure
We present a simple and intuitive framework for duality of locally compacts
groups, which is not based on the Haar measure. This is a map, functorial on a
non-degenerate subcategory, on the category of coinvolutive Hopf \cst-algebras,
and a similar map on the category of coinvolutive Hopf-von Neumann algebras. In
the \cst-version, this functor sends to and vice versa, for
every locally compact group . As opposed to preceding approaches, there is
an explicit description of commutative and co-commutative algebras in the range
of this map (without assumption of being isomorphic to their bidual): these
algebras have the form or respectively, where is a
locally compact group. The von Neumann version of the functor puts into
duality, in the group case, the enveloping von Neumann algebras of the algebras
above: and .Comment: To appear in Math. Scan
An example of a weighted algebra on uncountable group
We construct examples of weighted algebras with on
uncountable free groups. For no weighted algebras exist on these groups.
From the other side, we prove that an amenable group on which exist weighted
algebras with must be sigma-compact
On continuity of measurable group representations and homomorphisms
Let G be a locally compact group, and let U be its unitary representation on
a Hilbert space H. Endow the space L(H) of linear bounded operators on H with
weak operator topology. We prove that if U is a measurable map from G to L(H)
then it is continuous. This result was known before for separable H. To prove
this, we generalize a known theorem on nonmeasuralbe unions of point finite
families of null sets. We prove also that the following statement is consistent
with ZFC: every measurable homomorphism from a locally compact group into any
topological group is continuous. This relies, in turn, on the following
theorem: it is consistent with ZFC that for every null set S in a locally
compact group there is a set A such that AS is non-measurable.Comment: The previous version was not final, I update it once notice
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