Leavitt path algebras whose every Lie ideal is an ideal and applications

Time: 9:30 -- 11:00, May 24th, 2023.

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: In this talk, we classify all Leavitt path algebras which have the property that every Lie ideal is an ideal. We also give a necessary and sufficient condition for an ideal of an arbitrary Leavitt path algebra to be Lie solvable. As an application of the obtained results, we show that Leavitt path algebras with the property provide a class of locally finite, infinite-dimensional Lie algebras whose locally solvable radical is completely determined. This particularly gives us a new class of semisimple Lie algebras.