We introduce a new class of algebras called Poisson orders. This class includes the
symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of …

Let H be a Hopf algebra over the field k which is a finite module over a central affine sub-
Hopf algebra R. Examples include enveloping algebras U(\mathfrakg) of finite dimensional k …

In this paper, we provide a wildness criterion for any finite dimensional Hopf algebra with
finitely generated cohomology. This generalizes a result of Farnsteiner to not necessarily …

Discriminant ideals are defined for an algebraR with central subalgebra C and trace tr: R→
C. They are indexed by positive integers and more general than discriminants. Usually R is …

The two main approaches to the study of irreducible representations of orders (via traces
and Poisson orders) have so far been applied in a completely independent fashion. We …

We show how the existence of a PBW-basis and a large enough central subalgebra can be
used to deduce that an algebra is Frobenius. We apply this to rational Cherednik algebras …

We prove that a Hopf algebra with a finite coradical filtration is co-Frobenius. We also
characterize co-Frobenius Hopf algebras with coradical a Hopf subalgebra. Let H be a Hopf …

There are two main types of objects in the theory of cluster algebras: the upper cluster
algebras U with their Gekhtman–Shapiro–Vainshtein Poisson brackets and their root of unity …

We compute the center and Azumaya locus in the simplest non-abelian examples of
quantized multiplicative quiver varieties at a root of unity: quantum Weyl algebras of rank N …

Given an algebraically closed field k of characteristic p≥ 3, we classify the finite algebraic k-
groups whose algebras of measures afford a principal block of tame representation type …