Deformations of the five dimensional Heisenberg Lie algebra

In this note we explicitly give all the equivalent classes of deformations of the 5-dimensional Heisenberg Lie algebra $\mathfrak{h}_2$ over complex or real number fields. We show that there are altogether 20 infinitesimal deformations (families), 18 of them being extendable to real deformations and 2 of them are only infinitesimal.

Publication Details

Journal
ArXiv.org
Published
2025-04-20
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
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article

Deformations of the five dimensional Heisenberg Lie algebra

ArXiv.org
Homotopy and Cohomology in Algebraic Topology
article

Deformations of the five dimensional Heisenberg Lie algebra

article en

Abstract

In this note we explicitly give all the equivalent classes of deformations of the 5-dimensional Heisenberg Lie algebra $\mathfrak{h}_2$ over complex or real number fields. We show that there are altogether 20 infinitesimal deformations (families), 18 of them being extendable to real deformations and 2 of them are only infinitesimal.

ArXiv.org
Openalex Percentile: Top 44%
Homotopy and Cohomology in Algebraic Topology
Open Access PDFOpenAlex
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Deformations of the five dimensional Heisenberg Lie algebra · ArXiv.org (2025) | TGRS Research Map | TGRS