Let Q be a finite quiver without oriented cycles, let Λ be the associated preprojective algebra,
let g be the associated Kac–Moody Lie algebra with Weyl group W, and let n be the positive …

We investigate the variety of commuting matrices. We classify its components for any
number of matrices of size at most 7. We prove that starting from quadruples of 8× 8 …

SEMICANONICAL BASES AND PREPROJECTIVE ALGEBRAS Page 1 Ann. Scient. Éc.
Norm. Sup., 4e série, t. 38, 2005, p. 193 à 253. SEMICANONICAL BASES AND …

Each integrable lowest weight representation of a symmetrizable Kac-Moody Lie algebra g
has a crystal in the sense of Kashiwara, which describes its combinatorial properties. For a …

Inspired by recent work of Geiss–Leclerc–Schröer, we use Hom-finite cluster categories to
give a good candidate set for a basis of (upper) cluster algebras with coefficients arising …

Let $ Q $ be a finite quiver without oriented cycles, and let $\Lambda $ be the corresponding
preprojective algebra. Let $\mathfrak {g} $ be the Kac-Moody Lie algebra with Cartan datum …

Throughout, let K be an algebraically closed field of characteristic 0. We provide a generic
classification of locally free representations of Geiß-Leclerc-Schröer's algebras HK (C, D, Ω) …

We study the affine schemes of modules over gentle algebras. We describe the smooth
points of these schemes, and we also analyze their irreducible components in detail …

For any finite dimensional basic associative algebra, we study the presentation spaces and
their relation with the representation spaces. We prove two theorems about a general …

We study semicontinuous maps on varieties of modules over finite-dimensional algebras.
We prove that truncated Euler maps are upper or lower semicontinuous. This implies that 𝑔 …