The Leavitt path algebras of arbitrary graphs

• Autores: Gene Abrams , Gonzalo Aranda Pino
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 2, 2008, págs. 423-442
• Idioma: inglés
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• Resumen

  • We extend the notion of the Leavitt path algebra of a graph to include all directed graphs. We show how various ring-theoretic properties of these more general structures relate to the corresponding properties of Leavitt path algebras of row-finite graphs. Specifically, we identify those graphs for which the corresponding Leavitt path algebra is simple; purely infinite simple; exchange; and semiprime. In our final result, we show that all Leavitt path algebras have zero Jacobson radical.