Commutator Leavitt path algebras
Abstract
For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra LK(E) which lie in the commutator subspace [LK(E),LK(E)]. We then use this result to classify all Leavitt path algebras LK(E) that satisfy LK(E)=[LK(E),LK(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.
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