Algebra, Combinatorics and Number Theory

A Poisson Gel'fand-Kirillov problem in positive characteristic.

Speaker: 

César Lecoutre (Univ. of Kent - Canterbury, UK)

Date: 

Wednesday, 26 November, 2014 - 14:30

Venue: 

Math. Dep. (FC1), room 004

We study a problem of birational equivalence for polynomial Poisson algebras over a field of arbitrary characteristic. More precisely, the quadratic Gel'fand-Kirillov problem asks whether the field of fractions of a given polynomial Poisson algebra is isomorphic (as Poisson algebra) to a Poisson affine field, that is the field of fractions of a polynomial algebra (in several variables) where the Poisson bracket of two generators is equal to their product (up to a scalar). We answer positively this question for a large class of polynomial Poisson algebras and their Poisson prime quotients.

Enveloping skew fields of some super Lie algebras

Speaker: 

Jacques Alev (Université de Reims)

Date: 

Friday, 26 September, 2014 - 13:30

Venue: 

FCUP, Mathematics Building

In a previous paper, joint with François Dumas, we had studied a family of skew fields called "Mixed Weyl skew fields". Recently we realized that for certain particular values of the parameter these appear as enveloping skew fields of certain super Lie algebras, opening the way to a super analog of the Gelfand-Kirilllov Hypothesis.

 

Universal central extensions of Hom-Leibniz algebras

Speaker: 

Natalia Pacheco Rego (IPCA, Departamento de Ciências, Barcelos)

Date: 

Friday, 11 July, 2014 - 10:30

Venue: 

room 006 (FC1 -- Maths Bldg)

The main goal of this talk is to present the generalization of   classical results that characterize universal central extensions of Leibniz (Lie) algebras to the framework of Hom-Leinbiz (Hom-Lie) algebras.

In the category of Hom-Leibniz (Hom-Lie) algebras we introduce the notion of Hom-co-representation (Hom-L-module) as  adequate coefficients to construct the chain complex  from which we compute the Leibniz (Lie) homology of Hom-Leibniz (Hom-Lie) algebras.

Diagrammatic categorification

Speaker: 

Anne-Laure Thiel (Uppsala Univ./Sweden)

Date: 

Friday, 10 January, 2014 - 14:00

Venue: 

room 006 (FC1-Maths Building)

In a joint work with Marco Mackaay, we categorify the extended affine type A Hecke algebra and the affine quantum Schur algebra S(n,r) for 2 < r < n, using Elias-Khovanov and Khovanov-Lauda type diagrams.

Irreducible representations of groups associated with finite involutive algebras

Speaker: 

Carlos André

Date: 

Monday, 15 June, 2009 - 10:30

Venue: 

DMP, Room 0.04

An algebra group is a group of the form G = 1+J where J = J(A) is the Jacobson radical of a finite-dimensional associative algebra A (with identity). A Theorem of Z. Halasi asserts that, in the case where A is defined over a finite field F, every irreducible complex representation of G is induced...

Representations of differential operator algebras and their combinatorics

Speaker: 

Samuel Lopes (Universidade do Porto/CMUP)

Date: 

Friday, 14 December, 2012 - 15:00

Venue: 

Room 0.07, Mathematics building, FCUP

We consider the multiplication and differentiation operators x and d/dx, which generate the Weyl algebra. Fix a nonzero polynomial h=h(x) and let y be the operator h.d/dx, so that x and y satisfy the commutation relation [y, x]=h. The algebra generated by x and y is denoted by A_h and is a...

Ring epimorphisms and localisations with respect to a torsion class.

Speaker: 

Jorge Vitória (Universität Stuttgart)

Date: 

Wednesday, 19 December, 2012 - 14:30

Venue: 

Room 0.07, Mathematics building, FCUP

Ring epimorphisms are important from a representation-theoretical point of view as they provide a way to compare categories of modules. In this talk we will use the theory of localisations of rings and modules with respect to a torsion class (set up by Gabriel in his thesis) to construct ring...

Some new results related to Koethe’s nil ideal problem

Speaker: 

Edmund R.Puczylowski (Institute of Mathematics, University of Warsaw)

Date: 

Friday, 7 December, 2012 - 15:00

Venue: 

Room 0.06, Mathematics building, FCUP

It is easy to check that the sum of any family of two-sided nil ideals of an associative ring is a nil ideal as well. Does the same hold for left nil ideals? Though this question looks very elementary and was raised long ago (in 1930 by Koethe) it is still open. It is called Koethe’s nil ideal...

Injective hulls of simple modules over differential operator rings

Speaker: 

Can Hatipoglu (University of Porto)

Date: 

Friday, 30 November, 2012 - 15:00

Venue: 

Room 0.06, Mathematics building, FCUP

We consider rings over which the injective hulls of simple modules are locally Artinian. We will give an outline of the problem and talk about recent developments. In particular, we will see when the injective hulls of simple modules over an Ore extension R = K[x][y;d] are locally Artinian....

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