scholarly journals Proximity relations for real rank one valuations dominating a local regular ring

2003 ◽  
pp. 393-412 ◽  
Author(s):  
Ángel Granja ◽  
Cristina Rodríguez
Keyword(s):  
Regular Ring ◽  
Real Rank ◽  
Rank One

scholarly journals Amount of failure of upper-semicontinuity of entropy in non-compact rank-one situations, and Hausdorff dimension

2015 ◽  
Vol 37 (2) ◽  
pp. 539-563 ◽  
Author(s):  
S. KADYROV ◽  
A. POHL
Keyword(s):  
Hausdorff Dimension ◽  
Homogeneous Spaces ◽  
Upper Semicontinuity ◽  
Metric Entropy ◽  
Real Rank ◽  
Semisimple Lie Group ◽  
Uniform Lattice ◽  
Finite Center ◽  
Rank One ◽  
Set Of Points

Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $\unicode[STIX]{x1D6E4}\setminus G$, where $G$ is any connected semisimple Lie group of real rank one with finite center, and $\unicode[STIX]{x1D6E4}$ is any non-uniform lattice in $G$. We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points that diverge on average.

On the logarithmic derivative of zeta functions for compact even-dimensional locally symmetric spaces of real rank one

2019 ◽  
Vol 69 (2) ◽  
pp. 311-320 ◽  
Author(s):  
Muharem Avdispahić ◽  
Dženan Gušić
Keyword(s):  
Symmetric Spaces ◽  
Logarithmic Derivative ◽  
Zeta Functions ◽  
Real Rank ◽  
Locally Symmetric Spaces ◽  
Rank One ◽  
Approximate Formulas

Abstract We derive approximate formulas for the logarithmic derivative of the Selberg and the Ruelle zeta functions over compact, even-dimensional, locally symmetric spaces of real rank one. The obtained formulas are given in terms of zeta singularities.

scholarly journals Escape of mass and entropy for diagonal flows in real rank one situations

2015 ◽  
Vol 210 (1) ◽  
pp. 245-295 ◽  
Author(s):  
M. Einsiedler ◽  
S. Kadyrov ◽  
A. Pohl
Keyword(s):  
Real Rank ◽  
Rank One

scholarly journals Kuznetsov formulas for real rank one groups

1990 ◽  
Vol 93 (1) ◽  
pp. 171-206 ◽  
Author(s):  
R Miatello ◽  
N.R Wallach
Keyword(s):  
Real Rank ◽  
Rank One

scholarly journals Some Features of Rank One Real Solvable Cohomologically Rigid Lie Algebras with a Nilradical Contracting onto the Model Filiform Lie Algebra Qn

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 10 ◽  
Author(s):  
Rutwig Campoamor-Stursberg ◽  
Francisco Oviaño García
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Maximal Torus ◽  
Real Rank ◽  
Eigenvalue Spectrum ◽  
Generic Structure ◽  
Cohomology Space ◽  
Solvable Lie Algebras ◽  
Rank One ◽  
Filiform Lie Algebra

The generic structure and some peculiarities of real rank one solvable Lie algebras possessing a maximal torus of derivations with the eigenvalue spectrum spec ( t ) = 1 , k , k + 1 , ⋯ , n + k − 3 , n + 2 k − 3 for k ≥ 2 are analyzed, with special emphasis on the resulting Lie algebras for which the second Chevalley cohomology space vanishes. From the detailed inspection of the values k ≤ 5 , some series of cohomologically rigid algebras for arbitrary values of k are determined.

Ideal Structure of Multiplier Algebras of Simple C*-algebras With Real Rank Zero

2001 ◽  
Vol 53 (3) ◽  
pp. 592-630 ◽  
Author(s):  
Francesc Perera
Keyword(s):  
Stable Rank ◽  
Real Rank ◽  
Ideal Structure ◽  
Real Rank Zero ◽  
Von Neumann ◽  
Rank Zero ◽  
Rank One ◽  
A Chain ◽  
Multiplier Algebras ◽  
The Ideal

AbstractWe give a description of the monoid of Murray-von Neumann equivalence classes of projections for multiplier algebras of a wide class of σ-unital simple C*-algebras A with real rank zero and stable rank one. The lattice of ideals of this monoid, which is known to be crucial for understanding the ideal structure of themultiplier algebra , is therefore analyzed. In important cases it is shown that, if A has finite scale then the quotient of modulo any closed ideal I that properly contains A has stable rank one. The intricacy of the ideal structure of is reflected in the fact that can have uncountably many different quotients, each one having uncountably many closed ideals forming a chain with respect to inclusion.

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