932 research outputs found
Studies in fuzzy groups
In this thesis we first extend the notion of fuzzy normality to the notion of normality of a fuzzy subgroup in another fuzzy group. This leads to the study of normal series of fuzzy subgroups, and this study includes solvable and nilpotent fuzzy groups, and the fuzzy version of the Jordan-Hõlder Theorem. Furthermore we use the notion of normality to study products and direct products of fuzzy subgroups. We present a notion of fuzzy isomorphism which enables us to state and prove the three well-known isomorphism theorems and the fact that the internal direct product of two normal fuzzy subgroups is isomorphic to the external direct product of the same fuzzy subgroups. A brief discussion on fuzzy subgroups generated by fuzzy subsets is also presented, and this leads to the fuzzy version of the Basis Theorem. Finally, the notion of direct product enables us to study decomposable and indecomposable fuzzy subgroups, and this study includes the fuzzy version of the Remak-Krull-Schmidt Theorem
Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
We consider the Lie group generated by the Lie algebra
of -Minkowski space. Imposing the invariance of the metric under the
pull-back of diffeomorphisms induced by right translations in the group, we
show that a unique right invariant metric is associated with
. This metric coincides with the metric of de Sitter
space-time. We analyze the structure of unitary representations of the group
relevant for the realization of the non-commutative
-Minkowski space by embedding into -dimensional Heisenberg
algebra. Using a suitable set of generalized coherent states, we select the
particular Hilbert space and realize the non-commutative -Minkowski
space as an algebra of the Hilbert-Schmidt operators. We define dequantization
map and fuzzy variant of the Laplace-Beltrami operator such that dequantization
map relates fuzzy eigenvectors with the eigenfunctions of the Laplace-Beltrami
operator on the half of de Sitter space-time.Comment: 21 pages, v3 differs from version published in Fortschritte der
Physik by a note and references added and adjuste
Convergence of Fuzzy Tori and Quantum Tori for the quantum Gromov-Hausdorff Propinquity: an explicit approach
Quantum tori are limits of finite dimensional C*-algebras for the quantum
Gromov-Hausdorff propinquity, a metric defined by the author as a strengthening
of Rieffel's quantum Gromov-Hausdorff designed to retain the C*-algebraic
structure. In this paper, we propose a proof of the continuity of the family of
quantum and fuzzy tori which relies on explicit representations of the
C*-algebras rather than on more abstract arguments, in a manner which takes
full advantage of the notion of bridge defining the quantum propinquity.Comment: 41 Pages. This paper is the second half of ArXiv:1302.4058v2. The
latter paper has been divided in two halves for publications purposes, with
the first half now the current version of 1302.4058, which has been accepted
in Trans. Amer. Math. Soc. This second half is now a stand-alone paper, with
a brief summary of 1302.4058 and a new introductio
Level subsets and translations of QFST(G)
First, we introduce level subsets and translations of QFST(G) and study their properties. Secondly, we prove that the union and intersection of two-level subsets of QTST(G) are subgroups of G. Also we prove that translations of QTST(G) are also QFST(G). Finally, we define fuzzy image and fuzzy pre-image of translations of QFST(G) under group homomorphisms and anti group homomorphisms and investigate properties of them
The Reticulation of a Universal Algebra
The reticulation of an algebra is a bounded distributive lattice whose prime spectrum of filters or ideals is homeomorphic to the prime
spectrum of congruences of , endowed with the Stone topologies. We have
obtained a construction for the reticulation of any algebra from a
semi-degenerate congruence-modular variety in the case when the
commutator of , applied to compact congruences of , produces compact
congruences, in particular when has principal commutators;
furthermore, it turns out that weaker conditions than the fact that belongs
to a congruence-modular variety are sufficient for to have a reticulation.
This construction generalizes the reticulation of a commutative unitary ring,
as well as that of a residuated lattice, which in turn generalizes the
reticulation of a BL-algebra and that of an MV-algebra. The purpose of
constructing the reticulation for the algebras from is that of
transferring algebraic and topological properties between the variety of
bounded distributive lattices and , and a reticulation functor is
particularily useful for this transfer. We have defined and studied a
reticulation functor for our construction of the reticulation in this context
of universal algebra.Comment: 29 page
Hypermatrix factors for string and membrane junctions
The adjoint representations of the Lie algebras of the classical groups
SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric
products of two vector spaces, and hence are matrix representations. We
consider the analogous products of three vector spaces and study when they
appear as summands in Lie algebra decompositions. The Z3-grading of the
exceptional Lie algebras provide such summands and provides representations of
classical groups on hypermatrices. The main natural application is a formal
study of three-junctions of strings and membranes. Generalizations are also
considered.Comment: 25 pages, 4 figures, presentation improved, minor correction
Smarandache near-rings
The main concern of this book is the study of Smarandache analogue properties of near-rings and Smarandache near-rings; so it does not promise to cover all concepts or the proofs of all results
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