scholarly journals Anosov actions on noncommutative algebras

1994 ◽  
Vol 35 (11) ◽  
pp. 5582-5599 ◽  
Author(s):  
G. G. Emch ◽  
H. Narnhofer ◽  
W. Thirring ◽  
G. L. Sewell
Keyword(s):  
Noncommutative Algebras ◽  
Anosov Actions

scholarly journals Noncommutative algebras, context-free grammars and algebraic Hilbert series

2020 ◽  
Vol 101 ◽  
pp. 28-50
Author(s):  
Roberto La Scala ◽  
Dmitri Piontkovski ◽  
Sharwan K. Tiwari
Keyword(s):  
Hilbert Series ◽  
Noncommutative Algebras ◽  
Context Free ◽  
Context Free Grammars

scholarly journals Center of skew PBW extensions

2020 ◽  
Vol 30 (08) ◽  
pp. 1625-1650
Author(s):  
Oswaldo Lezama ◽  
Helbert Venegas
Keyword(s):  
Polynomial Type ◽  
Noncommutative Algebras ◽  
Skew Pbw Extensions

In this paper we compute the center of many noncommutative algebras that can be interpreted as skew [Formula: see text] extensions. We show that, under some natural assumptions on the parameters that define the extension, either the center is trivial, or, it is of polynomial type. As an application, we provided new examples of noncommutative algebras that are cancellative.

scholarly journals Gravity and the structure of noncommutative algebras

2006 ◽  
Vol 2006 (04) ◽  
pp. 054-054 ◽  
Author(s):  
Maja Burić ◽  
John Madore ◽  
Theodoros Grammatikopoulos ◽  
George Zoupanos
Keyword(s):  
Noncommutative Algebras

scholarly journals GUP-BASED AND SNYDER NONCOMMUTATIVE ALGEBRAS, RELATIVISTIC PARTICLE MODELS, DEFORMED SYMMETRIES AND INTERACTION: A UNIFIED APPROACH

2013 ◽  
Vol 28 (27) ◽  
pp. 1350131 ◽  
Author(s):  
SOUVIK PRAMANIK ◽  
SUBIR GHOSH
Keyword(s):  
Relativistic Particle ◽  
Generalized Uncertainty Principle ◽  
External Electromagnetic Field ◽  
Point Particle ◽  
Dynamical Analysis ◽  
Lagrangian Model ◽  
Nonlinear Constraints ◽  
Unified Approach ◽  
Deformed Symmetries ◽  
Noncommutative Algebras

We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space–time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

The Jacobi Matrix for Functions in Noncommutative Algebras

2014 ◽  
Vol 24 (4) ◽  
pp. 1059-1073
Author(s):  
Reiner Lauterbach ◽  
Gerhard Opfer
Keyword(s):  
Jacobi Matrix ◽  
Noncommutative Algebras

Transitivity of codimension-one Anosov actions of ℝk on closed manifolds

2010 ◽  
Vol 31 (1) ◽  
pp. 1-22 ◽  
Author(s):  
THIERRY BARBOT ◽  
CARLOS MAQUERA
Keyword(s):  
Unstable Foliation ◽  
Topologically Transitive ◽  
Codimension One ◽  
Ambient Manifold ◽  
Orientable Manifold ◽  
Anosov Actions ◽  
Anosov Flows ◽  
Dimension One

AbstractWe consider Anosov actions of ℝk, k≥2, on a closed connected orientable manifold M, of codimension one, i.e. such that the unstable foliation associated to some element of ℝk has dimension one. We prove that if the ambient manifold has dimension greater than k+2, then the action is topologically transitive. This generalizes a result of Verjovsky for codimension-one Anosov flows.

Non-abelian cohomology of abelian Anosov actions

2000 ◽  
Vol 20 (1) ◽  
pp. 259-288 ◽  
Author(s):  
ANATOLE KATOK ◽  
VIOREL NIŢICĂ ◽  
ANDREI TÖRÖK
Keyword(s):  
Discrete Time ◽  
Lie Group ◽  
Global Information ◽  
Infinite Dimensional ◽  
Anosov Actions ◽  
Geometric Character ◽  
Higher Rank ◽  
Real Analytic ◽  
A New Technique ◽  
Discrete Time Case

We develop a new technique for calculating the first cohomology of certain classes of actions of higher-rank abelian groups (${\mathbb Z}^k$ and ${\mathbb R}^k$, $k\ge 2$) with values in a linear Lie group. In this paper we consider the discrete-time case. Our results apply to cocycles of different regularity, from Hölder to smooth and real-analytic. The main conclusion is that the corresponding cohomology trivializes, i.e. that any cocycle from a given class is cohomologous to a constant cocycle. The principal novel feature of our method is its geometric character; no global information about the action based on harmonic analysis is used. The method can be developed to apply to cocycles with values in certain infinite dimensional groups and to rigidity problems.

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