Lie solvable Leavitt path algebras

摘要

We provide necessary and sufficient conditions on the graph E and the field K for which the Leavitt path algebra LK(E) is Lie solvable. Consequently, we obtain a complete description of Lie nilpotent Leavitt path algebras, and show that the Lie solvability of LK(E) and the Lie nilpotency of [LK(E),LK(E)] are the same. Furthermore, we compute the solvable index of a Lie solvable Leavitt path algebra.