The cohomological Hall algebra of a preprojective algebra

The Preprojective Algebra of a Modulated Graph

Geometry of Multiplicative Preprojective Algebra

Crawley-Boevey and Shaw recently introduced a certain multiplicative analogue of the deformed preprojective algebra, which they called the multiplicative preprojective algebra. In this paper we study the moduli space of (semi)stable representations of such an algebra (the multiplicative quiver variety), which in fact has many similarities to the quiver variety. We show that there exists a compl...

Arens regularity and cohomological properties of Banach lattice algebra

A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.

The Hall Algebra of a Cyclic Quiver

We show that the generic Hall algebra of nilpotent representations of an oriented cycle specialised at q = 0 is isomorphic to the generic extension monoid in the sense of Reineke. This continues the work of Reineke in [3]. 1. The generic extension monoid and the generic Hall algebra For the following let Q be a finite quiver with vertex set Q0 and arrow set Q1. We consider only finite dimension...

Cohomological Aspects of Hopf Algebra Liftings

A recent result of ours [GM] shows that all Hopf algebra liftings of a given diagram in the sense of Andruskiewitsch and Schneider are cocycle deformations of each other. Here we develop a ‘non-abelian’ cohomology theory, which gives a method for an explicit description of cocycles relevant to the lifting process. 0. Introduction The Nichols algebra B(V ) of a crossed kG-module V is a connected...