2021/01/24 by Josefina Barrionuevo, Barrionuevo, Josefina, Tirao, Paulo · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 17B30 #Rings and Algebras (math.RA) #Secondary 17B99
paper · pdf · doi:10.48550/arxiv.2101.09670
openalex publication_date 2021/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a novel construction of linear deformations for Lie algebras and use it to prove the non-rigidity of several classes of Lie algebras in different varieties. We consider the family of Lie algebras with an abelian factor showing that, in general, they are not rigid even for the case of a 1-dimensional abelian factor. We also address the problem of k-rigidity for k-step nilpotent Lie algebras. Using our construction and recent results in [BCC] we prove the that the k-step free nilpotent Lie algebras are k-rigid but not (k + 1)-rigid and that Heisenberg Lie algebras are 2-rigid but not 3-rigid.