## Logarithmic derivative and the Capelli identities (New developments in group representation theory and non-commutative h...

Published in Forum Mathematicum

If X is a quasi-compact and quasi-separated scheme, the category Qcoh(X) of quasi-coherent sheaves on X is locally finitely presented. Therefore categorical flat quasi-coherent sheaves in the sense of Stenström (1968) naturally arise. But there is also the standard definition of flatness in Qcoh(X) from the stalks. So it makes sense to wonder the r...

Published in Advances in Mathematics

Let Q be a finite quiver with vertex set I and arrow set Q1, k a field, and kQ its path algebra with its standard grading. This paper proves some category equivalences involving the quotient category QGr(kQ)≔Gr(kQ)/Fdim(kQ) of graded kQ-modules modulo those that are the sum of their finite dimensional submodules, namely QGr(kQ)≡ModS(Q)≡GrL(Q∘)≡ModL...

Published in Advances in Mathematics

In this paper, we prove the existence of isomorphisms between certain non-commutative algebras that are interesting from the representation theoretic perspective and arise as quantizations of certain Poisson algebras. We show that quantizations of Kleinian singularities obtained by three different constructions are isomorphic to each other. The con...

Published in Advances in Mathematics

A GR segment of an Artin algebra is a sequence of Gabriel–Roiter measures that is closed under direct successors and direct predecessors. The number of GR segments was conjectured to relate to the representation types of finite-dimensional hereditary algebras. We prove in the paper that a path algebra KQ of a finite connected acyclic quiver Q over ...

Published in Advances in Mathematics

Given a generically tame finite-dimensional algebra Λ over an infinite perfect field, we give, for each natural number d, parametrizations of the indecomposable Λ-modules with dimension d similar to those occurring for the algebraically closed field case. We parametrize over bounded principal ideal domains, instead of over rational algebras.

Let U be the enveloping algebra of a symmetric Kac-Moody algebra. The Weyl group acts on U, up to a sign. In addition, the positive subalgebra U^+ contains a so-called semicanonical basis, with remarkable properties. The aim of this paper is to show that these two structures are as compatible as possible.

For any truncated path algebra Λ, we give a structural description of the modules in the categories $${\mathcal{P}^{