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.
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.
Natalia Pacheco Rego (IPCA, Departamento de Ciências, Barcelos)
Friday, 11 July, 2014 - 10:30
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.
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.
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...
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 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...
Edmund R.Puczylowski (Institute of Mathematics, University of Warsaw)
Friday, 7 December, 2012 - 15:00
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...
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....