The No Gap Conjecture for tame hereditary algebras

On Ringel-hall Algebras of Tame Hereditary Algebras

The strong no loop conjecture for special biserial algebras

Let A be a finite dimensional algebra over a field given by a quiver with relations. Let S be a simple A-module with a non-split self-extension, that is, the quiver has a loop at the corresponding vertex. The strong no loop conjecture claims that S is of infinite projective dimension; see [1, 6]. This conjecture remains open except for monomial algebras; see, for example, [2, 6, 8, 11]. Under c...

On the Kostant Conjecture for Clifford Algebras

Let g be a complex simple Lie algebra, and h ⊂ g be a Cartan subalgebra. In the end of 1990s, B. Kostant defined two filtrations on h, one using the Clifford algebras and the odd analogue of the Harish-Chandra projection hcodd : Cl(g) → Cl(h), and the other one using the canonical isomorphism ȟ = h∗ (here ȟ is the Cartan subalgebra in the simple Lie algebra ǧ corresponding to the dual root syst...

The Breuil–mézard Conjecture for Quaternion Algebras

We formulate a version of the Breuil–Mézard conjecture for quaternion algebras, and show that it follows from the Breuil–Mézard conjecture for GL2. In the course of the proof we establish a mod p analogue of the Jacquet– Langlands correspondence for representations of GL2(k), k a finite field of characteristic p.

Hochschild Cohomology and Support Varieties for Tame Hecke Algebras

We give a basis for the Hochschild cohomology ring of tame Hecke algebras. We then show that the Hochschild cohomology ring modulo nilpotence is a finitely generated algebra of Krull dimension 2, and describe the support varieties of modules for these algebras.