Eighty-fourth BLOC meeting

BLOC

Bristol Leicester Oxford Colloquium

The 84th BLOC meeting will be held on 13 June 2019 at the University of Leicester.

Talks will take place in Ken Edwards Lecture Theatre 2.



 

Programme:

11:30 Marco Armenta (CIMAT Mexico)

Derived Invariance of operations in Hochschild theory.

12.30 Lunch

14.00 Cristian Chaparro Acosta (Buenos Aires)

The first Hochschild cohomology group of Brauer graph algebras with multiplicity one

15.00 Francesca Fedele (Newcastle)

Grothendieck groups of triangulated categories with higher cluster tilting subcategories

Tea

16.45 Javad Asadollahi (Isfahan)

nZ-Gorenstein cluster tilting subcategories

Please let Sibylle Schroll know if you are coming to the BLOC meeting, particularly if you wish to join us for lunch.


Abstracts

Marco Armenta (CIMAT, Mexico)

Title: Derived Invariance of operations in Hochschild theory.

Abstract: We prove that a derived equivalence between two finite dimensional algebras induces isomorphisms between Hochschild homology and Hochschild cohomology that respects simultaneously the cup product, the cap product, the Gerstenhaber bracket and the Connes differential. We do this with the use of Morita theory for derived categories and the cyclic functor defined by Keller to prove derived invariance of cyclic homology.

Javad Asadollahi (Isfahan)

Title: nZ-Gorenstein cluster tilting subcategories

Abstract: Let Λ be an artin algebra. In this talk, the notion of nZ-Gorenstein cluster tilting sub- categories will be introduced. We show that every nZ-cluster tilting subcategory of mod-Λ isnZ-Gorenstein if and only if Λ is an Iwanaga-Gorenstein algebra. Moreover, it will be shown that an nZ-Gorenstein cluster tilting subcategory of mod-Λ is an nZ-cluster tilting subcategory of the exact category Gprj-Λ, the subcategory of all Gorenstein projective objects of mod-Λ. Some basic properties of nZ-Gorenstein cluster tilting subcategories will be studied. In particular, we show that they are n-resolving subcategories, a higher version of resolving subcategories.

The talk is based on a joint work in preparation with R. Hafezi and S. Sadeghi.

 

Cristian Chaparro Acosta (Buenos Aires)

Title: The first Hochschild cohomology group of Brauer graph algebras with multiplicity one

Abstract: Brauer graph algebras with multiplicity one can be seen like the trivial extension of gentle algebras and the first Hochschild cohomology of the trivial extension of a finite dimensional algebra can be computed as a direct sum of four vector spaces. We compute the four vector spaces for the trivial extension of gentle algebras and give an explicit description of the Lie algebra structure of the first Hochschild cohomology group. This is a joint work with Sibylle Schroll and Andrea Solotar.

Francesca Fedele (Newcastle)

Title:Grothendieck groups of triangulated categories with higher cluster tilting subcategories

Abstract: Let C be a suitable triangulated category with a Serre functor and an n-cluster tilting subcategory T= add(t), for some integer n>1. In this setup, every indecomposable in T appears in a so called Auslander-Reiten (n+2)-angle in T. We show that the Grothendieck group of C can be expressed as a quotient of the split Grothendieck group of T by some elements determined by the Auslander-Reiten (n+2)-angles in T. We also apply this result to an example.


 

 

BLOC is supported by an LMS Scheme 3 grant, which is used to help offset travel costs for participants, with priority given to covering travel and accommodation costs for speakers and postgraduates.

Travel information is HERE.

Reimbursement: Please check with the organisers whether your travel costs can be reimbursed. If so then please download the following form, complete it and SIGN it and send it together with your original receipts and proof of travel to:

Prof Sibylle Schroll
Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH



For further information please contact one of the organisers:

Joe Chuang
Karin Erdmann
Jeremy Rickard
Sibylle Schroll

 

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