Quasi-classical Lie algebras and their contractions

Abstract

After classifying indecomposable quasi-classical Lie algebras in low dimension, and showing the existence of non-reductive stable quasi-classical Lie algebras, we focus on the problem of obtaining sufficient conditions for a quasi-classical Lie algebras to be the contraction of another quasi-classical algebra. It is illustrated how this allows to recover the Yang-Mills equations of a contraction by a limiting process, and how the contractions of an algebra may generate a parameterized families of Lagrangians for pairwise non-isomorphic Lie algebras.

17 pages, 2 Tables

Cited by in corpus (2)

• Non-geometric flux vacua, S-duality and algebraic geometry
• Classification of quadratic Lie algebras of low dimension