Commutator Leavitt path algebras

Abstract

For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras L_K(E) that satisfy L_K(E)=[L_K(E),L_K(E)]. We also show that these Leavitt path algebras have the additional (unusual) property that all their Lie ideals are (ring-theoretic) ideals, and construct examples of such rings with various ideal structures.

24 pages

References in corpus (1)

• Simple Lie algebras arising from Leavitt path algebras

Cited by in corpus (4)

• Simple Lie algebras arising from Leavitt path algebras
• Traces on Semigroup Rings and Leavitt Path Algebras
• Conjugacy and Least Commutative Congruences in Semigroups
• Leavitt path algebras in which every Lie ideal is an ideal and applications