Narrow positively graded Lie algebras

11 Dec 2017  ·  Millionshchikov Dmitry ·

We classify real and complex infinite-dimensional narrow positively graded Lie algebras ${\mathfrak g}=\oplus_{i=1}^{{+}\infty}{\mathfrak g}_i$ with properties $$ [{\mathfrak g}_1, {\mathfrak g}_i]={\mathfrak g}_{i{+}1}, \; \dim{{\mathfrak g}_i}+\dim{{\mathfrak g}_{i{+}1}} \le 3, \; i \ge 1. $$ 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. read more

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Rings and Algebras