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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Presented by: Kenneth Goodearl.
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Mesyan, Z. Commutator Leavitt Path Algebras. Algebr Represent Theor 16, 1207–1232 (2013). https://doi.org/10.1007/s10468-012-9352-4
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DOI: https://doi.org/10.1007/s10468-012-9352-4