Introduction
This intensive research programme aims to bring together top-level researchers in geometry, algebra, and topology with a particular focus on how these areas interact. The idea grew from the recently founded “Laboratory of Interactions between Geometry, Algebra, and Topology (LIGAT)” based at the Universitat Autònoma de Barcelona (UAB). The programme will consist of eight weeks of different activities conducted by senior research visitors and local researchers from the LIGAT. There will be an advanced course consisting of different lecture series on a variety of topics. These courses are ideal for PhD students and young researchers and participants will also have the opportunity to present their own work. The central part of the programme is a series of workshops on selected topics in geometry, algebra, and topology. The programme is completed by weekly seminars, promoting interactions and collaborations among participants and facilitating communication between the different research directions. All together, we aim to promote high level and quality research in diverse but interrelated areas of research, and to facilitate the inclusion of younger researchers in these areas.
Organising Committee
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Florent Balacheff
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Universitat Autònoma de Barcelona
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Carles Broto
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Universitat Autònoma de Barcelona
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| John Greenlees | University of Warwick |
| Francesc Perera | Universitat Autònoma de Barcelona |
Main activities of the programme
Related activities
Title: The injective Leavitt complex
Huanhuan Li
Abstract: For a finite graph E without sinks, we consider the corresponding finite dimensional algebra A with radical square zero. We construct an explicit compact generator for the homotopy category of acyclic complexes of injective A-modules. We call such a generator the injective Leavitt complex of E. This terminology is justified by the following result: the differential graded endomorphism algebra of the injective Leavitt complex of E is quasi-isomorphic to the Leavitt path algebra of E. Here, the Leavitt path algebra is naturally Z-graded and viewed as a differential graded algebra with trivial differential.
12:05-12:55
Title: The talented monoid of a Leavitt path algebra
Roozbeh Hazrat
Abstract. There is a tight relation between the geometry of a directed graph and the algebraic structure of a Leavitt path algebra associated to it. We show a similar connection between the geometry of the graph and the structure of a certain monoid associated to it. This monoid is isomorphic to the positive cone of the graded K0-group of the Leavitt path algebra which is naturally equipped with a Z-action. As an example, we show that a graph has a cycle without an exit if and only if the monoid has a periodic element. Consequently a graph has Condition (L) if and only if the group Z acts freely on the monoid. We go on to show that the algebraic structure of Leavitt path algebras (such as simplicity, purely infinite simplicity, or the lattice of ideals) can be described completely via this monoid. Therefore an isomorphism between the monoids (or graded K0’s) of two Leavitt path algebras implies that the algebras have similar algebraic structures. These all confirm that the graded Grothendieck group could be a sought-after complete invariant for the classification of Leavitt path algebras.
This is joint work with Huanhuan Li.
LIST OF PARTICIPANTS
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INVOICE/PAYMENT INFORMATION
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Paying by credit card
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LODGING INFORMATION
ON-CAMPUS AND BELLATERRA
BARCELONA AND OFF-CAMPUS
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For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at nhernandez@crm.cat
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