Twist deformations for generalized Heisenberg algebras

TL;DR

This paper explores how multidimensional Heisenberg algebras can be deformed using chains of Jordanian twists within simple Lie algebras, revealing complex structures in their deformations.

Contribution

It introduces a method to analyze deformations of multidimensional Heisenberg algebras via extended Jordanian twists in simple Lie algebras, especially U(sl(N)).

Findings

Deformation spectra can be studied using chains of extended Jordanian twists.

In U(sl(N)) for N>5, two-dimensional Heisenberg subalgebras have nine deformed costructures.

Deformations are interconnected by internal and external twists forming a commutative diagram.

Abstract

Multidimensional Heisenberg algebras, whose creation and annihilation operators are the N-dimensional vectors, can be injected into simple Lie algebras g. It is demonstrated that the spectrum of their deformations can be investigated using chains of extended Jordanian twists applied to U(g). In the case of U(sl(N)) (for N>5) the two-dimensional Heisenberg subalgebras have nine deformed costructures connected by four "internal" and "external" twists composing the commutative diagram.