### Abstract

Original language | English |
---|---|

Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Journal of Geometry and Physics |

Volume | 125 |

Publication status | Published - 2018 |

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### All Science Journal Classification (ASJC) codes

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology

### Cite this

*Journal of Geometry and Physics*,

*125*, 1-11.

**A description of pseudo-bosons in terms of nilpotent Lie algebras.** / Bagarello, Fabio; Russo, Francesco G.; Bagarello, Fabio.

Research output: Contribution to journal › Article

*Journal of Geometry and Physics*, vol. 125, pp. 1-11.

}

TY - JOUR

T1 - A description of pseudo-bosons in terms of nilpotent Lie algebras

AU - Bagarello, Fabio

AU - Russo, Francesco G.

AU - Bagarello, Fabio

PY - 2018

Y1 - 2018

N2 - We show how the one-mode pseudo-bosonic ladder operators provide concrete examples of nilpotent Lie algebras of dimension five. It is the first time that an algebraic–geometric structure of this kind is observed in the context of pseudo-bosonic operators. Indeed we do not find the well known Heisenberg algebras, which are involved in several quantum dynamical systems, but different Lie algebras which may be decomposed into the sum of two abelian Lie algebras in a prescribed way. We introduce the notion of semidirect sum (of Lie algebras) for this scope and find that it describes very well the behavior of pseudo-bosonic operators in many quantum models.

AB - We show how the one-mode pseudo-bosonic ladder operators provide concrete examples of nilpotent Lie algebras of dimension five. It is the first time that an algebraic–geometric structure of this kind is observed in the context of pseudo-bosonic operators. Indeed we do not find the well known Heisenberg algebras, which are involved in several quantum dynamical systems, but different Lie algebras which may be decomposed into the sum of two abelian Lie algebras in a prescribed way. We introduce the notion of semidirect sum (of Lie algebras) for this scope and find that it describes very well the behavior of pseudo-bosonic operators in many quantum models.

UR - http://hdl.handle.net/10447/298849

UR - http://www.elsevier.com/locate/geomphys

M3 - Article

VL - 125

SP - 1

EP - 11

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

ER -