On the presence of families of pseudo-bosons in nilpotent Lie algebras of arbitrary corank

Abstract

We have recently shown that pseudo-bosonic operators realize concrete examples of finite dimensional nilpotent Lie algebras over the complex field. It has been the first time that such operators were analyzed in terms of nilpotent Lie algebras (under prescribed conditions of physical character). On the other hand, the general classification of a finite dimensional nilpotent Lie algebra $\mathfrak{l}$ may be given via the size of its Schur multiplier involving the so-called corank $t(\mathfrak{l})$ of $\mathfrak{l}$. We represent $\mathfrak{l}$ by pseudo-bosonic ladder operators for $t(\mathfrak{l})\le 6$ and this allows us to represent $\mathfrak{l}$ when its dimension is $\le 5$.

Accepted in Journal of Geometry and Physics

References in corpus (1)

• A description of pseudo-bosons in terms of nilpotent Lie algebras

Cited by in corpus (3)

• Topological decompositions of the Pauli group and their influence on dynamical systems
• Realization of Lie algebras of high dimension via pseudo-bosonic operators
• Some Consequences of the Grunewald-O'Halloran Conjecture for Pseudoquonic Operators