Analysis in Noncommutative Algebras and Modules

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.

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Gravity and the structure of noncommutative algebras

Journal of High Energy Physics ◽

10.1088/1126-6708/2006/04/054 ◽

2006 ◽

Vol 2006 (04) ◽

pp. 054-054 ◽

Cited By ~ 34

Author(s):

Maja Burić ◽

John Madore ◽

Theodoros Grammatikopoulos ◽

George Zoupanos

Keyword(s):

Noncommutative Algebras

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Anosov actions on noncommutative algebras

Journal of Mathematical Physics ◽

10.1063/1.530766 ◽

1994 ◽

Vol 35 (11) ◽

pp. 5582-5599 ◽

Cited By ~ 41

Author(s):

G. G. Emch ◽

H. Narnhofer ◽

W. Thirring ◽

G. L. Sewell

Keyword(s):

Noncommutative Algebras ◽

Anosov Actions

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

International Journal of Modern Physics A ◽

10.1142/s0217751x13501315 ◽

2013 ◽

Vol 28 (27) ◽

pp. 1350131 ◽

Cited By ~ 22

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.

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