Infinite dimensional analogues of nilpotent and solvable Lie algebras
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：Bakhrom Omirov (Harbin Institute of Technology)
： 2026-01-13 16:30
：Conference Room C503 at Administration Building at Haiyun Campus
Speaker：Bakhrom Omirov (Harbin Institute of Technology)
Time：2026-1-13 16:30
Location：Conference Room C503 at Administration Building at Haiyun Campus
Abstract:
The talk is devoted to infinite-dimensional analogues of nilpotent and solvable Lie algebras, focusing on the classes of pro-nilpotent, residually nilpotent, pro-solvable and residually solvable Lie algebras. We show that classical triangularization results such as Engel's and Lie's theorems are extendable to the pro-setting and establish existence results for the pro-nilpotent radical in pro-solvable algebras and in certain residually solvable algebras. We adapt finite-dimensional construction methods to produce residually solvable extensions with a given pro-nilpotent radical under natural finiteness conditions. By analyzing derivations and maximal tori of pro-nilpotent algebras, we extend the notion of rank and show that, for pro-nilpotent algebras of maximal rank, every derivation of a maximal residually solvable extension is inner. Finally, we describe standard constructions such as tensor products, direct sums, and central extensions, that preserve pro-nilpotency.
