Commutator Leavitt Path Algebras |
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Authors: | Zachary Mesyan |
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Institution: | 1. Department of Mathematics, University of Colorado, Colorado Springs, CO, 80918, USA
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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. |
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