scholarly journals FREDHOLM MODULES OVER GRAPH -ALGEBRAS

2015 ◽  
Vol 92 (2) ◽  
pp. 302-315
Author(s):  
TYRONE CRISP
Keyword(s):  
Finite Rank ◽  
Homology Class ◽  
Lens Spaces ◽  
Graph Algebras ◽  
Explicit Formulas ◽  
Fredholm Module

We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in $K$-homology of graph $C^{\ast }$-algebras. We prove that every $K$-homology class for such an algebra is represented by a Fredholm module having finite-rank commutators, and we exhibit generating Fredholm modules for the $K$-homology of quantum lens spaces.

RESHETIKHIN–TURAEV INVARIANTS OF SEIFERT 3-MANIFOLDS FOR CLASSICAL SIMPLE LIE ALGEBRAS

2004 ◽  
Vol 13 (05) ◽  
pp. 617-668 ◽  
Author(s):  
SØREN KOLD HANSEN ◽  
TOSHIE TAKATA
Keyword(s):  
Lie Algebras ◽  
Lens Spaces ◽  
Quantum Level ◽  
Explicit Formulas ◽  
Standard Data ◽  
Finite Dimensional ◽  
Seifert Manifolds ◽  
Arbitrary Complex ◽  
Large Quantum

We derive explicit formulas for the Reshetikhin–Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra [Formula: see text] in terms of the Seifert invariants and standard data for [Formula: see text]. A main corollary is a determination of the full asymptotic expansions of these invariants for lens spaces in the limit of large quantum level. This result is in agreement with the asymptotic expansion conjecture due to Andersen [1,2].

scholarly journals Quantum lens spaces and graph algebras

2003 ◽  
Vol 211 (2) ◽  
pp. 249-263 ◽  
Author(s):  
Jeong Hee Hong ◽  
Wojciech Szymański
Keyword(s):  
Lens Spaces ◽  
Graph Algebras

Isometry classes of 3 dimensional lens spaces

2002 ◽  
Vol 13 (7) ◽  
pp. 295-299
Author(s):  
Michel Cahen ◽  
Mohamed Chaibi
Keyword(s):  
Lens Spaces ◽  
3 Dimensional

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

scholarly journals Dimension of the Exceptional Set in the Aronszajn–Donoghue Theorem for Finite Rank Perturbations

2020 ◽  
Author(s):  
Constanze Liaw ◽  
Sergei Treil ◽  
Alexander Volberg
Keyword(s):  
Finite Rank ◽  
Measure Zero ◽  
Adjoint Operator ◽  
Cyclic Vector ◽  
Spectral Measures ◽  
Hermitian Matrices ◽  
Exceptional Set ◽  
Direct Sum ◽  
Rank One Perturbation ◽  
Rank One

Abstract The classical Aronszajn–Donoghue theorem states that for a rank-one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the original and perturbed operators are mutually singular. As simple direct sum type examples show, this result does not hold for finite rank perturbations. However, the set of exceptional perturbations is pretty small. Namely, for a family of rank $d$ perturbations $A_{\boldsymbol{\alpha }}:= A + {\textbf{B}} {\boldsymbol{\alpha }} {\textbf{B}}^*$, ${\textbf{B}}:{\mathbb C}^d\to{{\mathcal{H}}}$, with ${\operatorname{Ran}}{\textbf{B}}$ being cyclic for $A$, parametrized by $d\times d$ Hermitian matrices ${\boldsymbol{\alpha }}$, the singular parts of the spectral measures of $A$ and $A_{\boldsymbol{\alpha }}$ are mutually singular for all ${\boldsymbol{\alpha }}$ except for a small exceptional set $E$. It was shown earlier by the 1st two authors, see [4], that $E$ is a subset of measure zero of the space $\textbf{H}(d)$ of $d\times d$ Hermitian matrices. In this paper, we show that the set $E$ has small Hausdorff dimension, $\dim E \le \dim \textbf{H}(d)-1 = d^2-1$.

On a generalization of the Rényi–Srivastava characterization of the Poisson law

2021 ◽  
Vol 58 (1) ◽  
pp. 68-82
Author(s):  
Jean-Renaud Pycke
Keyword(s):  
Life Insurance ◽  
Collective Model ◽  
New Method ◽  
Bell Polynomials ◽  
Explicit Formulas ◽  
Compound Distributions ◽  
Poisson Law ◽  
Pierre Loti

AbstractWe give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generalization of a characterization of Poisson law due to Rényi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions occurring in the extended collective model in non-life insurance.

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