Martin Herschend

Selfinjective quivers with potential and 2-representation-finite algebras

We study quivers with potential (QPs) whose Jacobian algebras are finite-dimensional selfinjective. They are an analogue of the ‘good QPs’ studied by Bocklandt whose Jacobian algebras are 3-Calabi–Yau. We show that 2-representation-finite algebras are truncated Jacobian algebras of selfinjective QPs, which are factor algebras of Jacobian algebras by certain sets of arrows called cuts. We show that selfinjectivity of QPs is preserved under iterated mutation with respect to orbits of the Nakayama permutation. We give a sufficient condition for all truncated Jacobian algebras of a fixed QP to be derived equivalent. We introduce planar QPs which provide us with a rich source of selfinjective QPs.

n-representation-finite algebras and twisted fractionally Calabi–Yau algebras

In this short paper, we study

On the representation ring of the polynomial algebra over a perfect field

n

n-representation infinite algebras

-representation-finite algebras from the viewpoint of the fractionally Calabi-Yau property. We shall show that all

On the Representation Ring of a Quiver

n

Representation theory of Geigle-Lenzing complete intersections

-representation-finite algebras are twisted fractionally Calabi-Yau. We also show that for any

Tensor products on quiver representations

\ell>0

In which dimensions does a division algebra over a given ground field exists

, twisted

On the representation rings of quivers of exceptional Dynkin type

\frac{n(\ell-1)}{\ell}

Galois coverings and the Clebsch-Gordan problem for quiver representations

-Calabi-Yau algebras of global dimension at most