dc.contributor.author Abrams, Gene dc.date.accessioned 2014-06-18T08:15:56Z dc.date.available 2014-06-18T08:15:56Z dc.date.created 2014-06-18 dc.date.issued 2014-06-18 dc.identifier.uri http://hdl.handle.net/10630/7688 dc.description.abstract Let $E = (E^0, E^1, s,r)$ be an arbitrary directed graph (i.e., no restriction is placed on the cardinality of $E^0$, or of $E^1$, or of $s^{-1}(v)$ for $v\in E^0$). Let $L_K(E)$ denote the Leavitt path algebra of $E$ with coefficients in a field $K$, and let $C^*(E)$ denote the graph C$^*$-algebra of $E$. es_ES % (Note: here $C^*(E)$ need not be separable.) We give necessary and sufficient conditions on $E$ so that $L_K(E)$ is primitive. (This is joint work with Jason Bell and K.M. Rangaswamy.) We then show that these same conditions are precisely the necessary and sufficient conditions on $E$ so that $C^*(E)$ is primitive. (This is joint work with Mark Tomforde.) This situation gives yet another example of algebraic / analytic properties of the graph algebras $L_K(E)$ and $C^*(E)$ for which the graph conditions equivalent to said property are identical, but for which the proof / techniques used are significantly different. In the Leavitt path algebra setting, we show how this result allows for the easy construction of a large collection of prime, non-primitive von Neumann regular algebras (thereby giving a systematic answer to a decades-old question of Kaplansky). In the graph C$^*$-algebra setting, we show how this result allows for the easy construction of a large collection of prime, non-primitive C$^*$-algebras (thereby giving a systematic answer to a decades-old question of Dixmier). dc.description.sponsorship Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. es_ES dc.language.iso eng es_ES dc.rights info:eu-repo/semantics/openAccess es_ES dc.title Primitive graph algebras es_ES dc.type info:eu-repo/semantics/conferenceObject es_ES dc.centro Facultad de Ciencias es_ES dc.relation.eventtitle Conferencia del profesor Gene Abrams es_ES dc.relation.eventplace Aula Jacques Louis Lions. Facultad de Ciencias. Universidad de Málaga. es_ES dc.relation.eventdate Martes 24 de junio de 2014 es_ES
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