Narrow positively graded Lie algebras

2017/12/11 by Millionshchikov, Dmitry
#17B30 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1712.03718

Abstract

We classify real and complex infinite-dimensional narrow positively graded Lie algebras \mathfrak g=⊕_i=1^+∞\mathfrak g_i with properties [\mathfrak g₁, \mathfrak g_i]=\mathfrak g_i+1, dim\mathfrak g_i+dim\mathfrak g_i+1 ≤ 3, i ≥ 1. In the proof of the main theorem we apply successive central extensions of finite-dimensional Carnot algebras. In sub-Riemannian geometry, control theory, and geometric group theory, Carnot algebras play a significant role.

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