1,357 research outputs found
From C*algebra extensions to CQMS, , Podles sphere and other examples
We construct compact quantum metric spaces (CQMS) starting with some
C*algebra extension with a positive splitting. As special cases we discuss the
case of Toeplitz algebra, quantum SU(2) and Podles sphere
Metrics On The Quantum Heisenberg Manifold
Compact quantum metric spaces are order unit spaces along with a Lip norm. On
the order unit space of the selfadjoint elements of the dense subalgebra of
smooth elements in the quantum Heisenberg manifold we construct Lip norms
Connes' calculus for The Quantum double suspension
Given a spectral triple Connes associated a
canonical differential graded algebra .
However, so far this has been computed for very few special cases. We identify
suitable hypotheses on a spectral triple that helps one to compute the
associated Connes' calculus for its quantum double suspension. This allows one
to compute for spectral triples obtained by iterated
quatum double suspension of the spectral triple associated with a first order
differential operator on a compact smooth manifold. This gives the first
systematic computation of Connes' calculus for a large family of spectral
triples
Gelfand-Kirillov dimension of the algebra of regular functions on quantum groups
Let be the -deformation of a simply connected simple compact Lie
group of type , or and be the algebra of
regular functions on . In this article, we prove that the Gelfand-Kirillov
dimension of is equal to the dimension of real manifold .Comment: 15 pages. arXiv admin note: text overlap with arXiv:1709.0858
Optimal Covering with Mobile Sensors in an Unbounded Region
Covering a bounded region with minimum number of homogeneous sensor nodes is
a NP-complete problem \cite{Li09}. In this paper we have proposed an {\it id}
based distributed algorithm for optimal coverage in an unbounded region. The
proposed algorithm guarantees maximum spreading in rounds without
creating any coverage hole. The algorithm executes in synchronous rounds
without exchanging any message.
We have also explained how our proposed algorithm can achieve optimal energy
consumption and handle random sensor node deployment for optimal spreading.Comment: 7 pages, submitted in the Eighth International Conference on Wireless
Communication and Sensor Networks (WCSN-2012
Equivalence of Two Approaches to Yang-Mills on Non-commutative Torus
There are two notions of Yang-Mills action functional in noncommutative
geometry. We show that for noncommutative n-torus both these notions agree. We
also prove a structure theorem on the Hermitian structure of a finitely
generated projective modules over spectrally invariant subalgebras of
-algebras
Characterization of spectral triples: A combinatorial approach
We describe a general technique to study Dirac operators on noncommutative
spaces under some additional assumptions. The main idea is to capture the
compact resolvent condition in a combinatorial set up. Using this, we then
prove that for a certain class of representations of the C^*-algebra
C(SU_q(\ell+1)), any Dirac operator that diagonalises with respect to the
natural basis of the underlying Hilbert space must have trivial sign.Comment: v3: partly rewritten; the equivariant case has now been taken out and
would be treated in a separate paper. v2: few typos corrected. LaTeX2e, uses
xy-pic and eepi
Multi-Use Multi-Secret Sharing Scheme for General Access Structure
The main aim of this paper is to construct a multi-secret sharing scheme for
general access structure in a trusted dealer model using suitable hash function
and Lagrange's interpolation method. Even though, the proposed scheme is a
multi-secret and multi-use one, each participant has to carry only one share.
The suitable use of collision resistant one way hash function makes the scheme
efficient and multi-use. Moreover, the scheme has a nice property that secrets,
participants or qualified sets of participants may be added to or even may be
made inactive dynamically by the dealer to get a new access structure without
altering the shares of the existing participants in the old access structure.
Finally, in the proposed scheme, both the combiner and the share holders can
verify the correctness of the information that they are receiving from each
other
K-groups of the quantum homogeneous space
Quantum Steiffel manifolds were introduced by Vainerman and Podkolzin in
\cite{VP}. They classified the irreducible representations of their underlying
-algebras. Here we compute the K groups of the quantum homogeneous spaces
. Specializing to the case we show that
the fundamental unitary for quantum is nontrivial and is a unimodular
element in
Characterization of -equivariant spectral triples for the odd dimensional quantum spheres
The quantum group has a canonical action on the odd
dimensional sphere . All odd spectral triples acting on the
space of and equivariant under this action have been
characterized. This characterization then leads to the construction of an
optimum family of equivariant spectral triples having nontrivial -homology
class. These generalize the results of Chakraborty & Pal for .Comment: LaTeX2e, 20 page
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