Deformations of the five dimensional Heisenberg Lie algebra

2025/04/20 by Fialowski, Alice, Mandal, Ashis
#17B56 #B81 #B99 #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2504.14647

Abstract

In this note we explicitly give all the equivalent classes of deformations of the 5-dimensional Heisenberg Lie algebra \mathfrakh₂ 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.

Citations

• The moduli space of complex 5-dimensional Lie algebras
• Solvable Lie A-algebras
• Leibniz algebra deformations of a Lie algebra

Related

• Complete Structural Analysis of q-Heisenberg Algebras: Homology, Rigidity, Automorphisms, and Deformations
• Lie algebras : Classification, Deformations and Rigidity
• Lie Atoms and their deformation theory
• Leibniz algebra deformations of a Lie algebra
• Deformations and rigidity in varieties of Lie algebras