5,485 research outputs found
Interval valued (\in,\ivq)-fuzzy filters of pseudo -algebras
We introduce the concept of quasi-coincidence of a fuzzy interval value with
an interval valued fuzzy set. By using this new idea, we introduce the notions
of interval valued (\in,\ivq)-fuzzy filters of pseudo -algebras and
investigate some of their related properties. Some characterization theorems of
these generalized interval valued fuzzy filters are derived. The relationship
among these generalized interval valued fuzzy filters of pseudo -algebras
is considered. Finally, we consider the concept of implication-based interval
valued fuzzy implicative filters of pseudo -algebras, in particular, the
implication operators in Lukasiewicz system of continuous-valued logic are
discussed
Beyond fuzzy spheres
We study polynomial deformations of the fuzzy sphere, specifically given by
the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the
Poisson structure on a surface in . We find that several
surfaces, differing by constants, are described by the Higgs algebra at the
fuzzy level. Some of these surfaces have a singularity and we overcome this by
quantizing this manifold using coherent states for this nonlinear algebra. This
is seen in the measure constructed from these coherent states. We also find the
star product for this non-commutative algebra as a first step in constructing
field theories on such fuzzy spaces.Comment: 9 pages, 3 Figures, Minor changes in the abstract have been made. The
manuscript has been modified for better clarity. A reference has also been
adde
Quantized Nambu-Poisson Manifolds and n-Lie Algebras
We investigate the geometric interpretation of quantized Nambu-Poisson
structures in terms of noncommutative geometries. We describe an extension of
the usual axioms of quantization in which classical Nambu-Poisson structures
are translated to n-Lie algebras at quantum level. We demonstrate that this
generalized procedure matches an extension of Berezin-Toeplitz quantization
yielding quantized spheres, hyperboloids, and superspheres. The extended
Berezin quantization of spheres is closely related to a deformation
quantization of n-Lie algebras, as well as the approach based on harmonic
analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms
of foliations of R^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative
hyperplanes. Some applications to the quantum geometry of branes in M-theory
are also briefly discussed.Comment: 43 pages, minor corrections, presentation improved, references adde
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