Dynamical Systems and Quantum Bicrossproduct Algebras

TL;DR

This paper explores the structure of quantum bicrossproduct algebras related to inhomogeneous Lie algebras, revealing how their nonlinear actions generate dynamical systems linked to translations.

Contribution

It provides a unified analysis of quantum bicrossproduct algebras and introduces a method to associate dynamical systems with each generator via nonlinear actions.

Findings

Establishment of a nonlinear action framework for quantum bicrossproduct algebras.

Connection of generators to dynamical systems through these nonlinear actions.

Unified approach applicable to Poincare, Galilei, and Euclidean algebras.

Abstract

We present a unified study of some aspects of quantum bicrossproduct algebras of inhomogeneous Lie algebras, like Poincare, Galilei and Euclidean in N dimensions. The action associated to the bicrossproduct structure allows to obtain a nonlinear action over a new group linked to the translations. This new nonlinear action associates a dynamical system to each generator which is the object of study in this paper.