Eighty-second BLOC meeting

BLOC

Bristol Leicester Oxford Colloquium

The 82nd BLOC meeting will be held on Friday 8th February 2019 at the Mathematical Institute in Oxford.

Programme:

12.00 Hipolito Treffinger (Leicester) An algebraic approach to Harder-Narasimhan filtrations

13.00 Lunch

15.00 Andrea Solotar (Buenos Aires) Hochschild cohomology and Gerstenhaber bracket of a family of subalgebras of the Weyl algebra

Tea

16.45 Ken Brown (Glasgow) Commutative-by-finite Hopf algebras

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


Abstracts

Hipolito Treffinger: Stability conditions are important tools that have shown great potential in various branches of mathematics.

One of the main properties of stability conditions is the following. Given a stability condition defined over a category, every object in this category is filtered by some distinguished objects called semi-stables. This filtration, that is unique up-to-isomorphism, is know as the Harder-Narasimhan filtration. One less studied property of stability conditions, when defined over an abelian category, is the fact that each of them induce a chain of torsion classes that is naturally indexed.

In this talk we will study arbitrary indexed chain of torsion classes. Our first result states that every indexed chain of torsion classes induce a Harder- Narasimhan filtration. Afterwards, we follow ideas from Bridgeland to show that the set of all indexed chain of torsion classes satisfying a mild technical condition form a topological space. If there is enough time we will characterise the neighbourhood or some distinguished points.

Andrea Solotar: For a polynomial h(x) in F[x], where F is any field, let A be the F-algebra given by generators x and y and relation [y, x] = h. This family of algebras include the Weyl algebra, enveloping algebras of 2-dimensional Lie algebras, the Jordan plane and several other interesting subalgebras of the Weyl algebra.

In a joint work in progress with Samuel Lopes, we computed the Hochschild cohomology HH(A) of A and determined explicitly the Gerstenhaber structure of HH(A), as a Lie module over the Lie algebra HH1(A). In case F has characteristic 0, this study has revealed that HH(A) has finite length as a Lie module over HH1(A) with pairwise non-isomorphic composition factors and the latter can be naturally extended into irreducible representations of the Virasoro algebra. Moreover, the whole action can be understood in terms of the partition formed by the multiplicities of the irreducible factors of the polynomial h.

Ken Brown: Roughly speaking, a commutative-by-finite Hopf algebra is a Hopf algebra which is an extension of a commutative Hopf algebra by a finite dimensional Hopf algebra. There are many big and significant classes of such algebras (beyond of course the commutative ones and the finite dimensional ones!). I’ll make the definition precise, discuss examples and review results, some old and some new. No previous knowledge of Hopf algebras is necessary.

 


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.

There will be time for informal discussions during the meeting.


For further information please contact one of the organisers:

Joe Chuang
Karin Erdmann
Jeremy Rickard
Sibylle Schroll

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