Published in manuscripta mathematica
In the setting of a variety X admitting a tilting bundle T we consider the problem of constructing X as a quiver GIT quotient of the algebra A:=EndX(T)op\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddside...
Published in Algebras and Representation Theory
We complete a derived equivalence classification of the gentle two-cycle algebras initiated in earlier papers by Avella-Alaminos and Bobinski–Malicki.
Published in Frontiers of Mathematics in China
Let n ≥ 3. The complex Lie algebra, which is attached to a unit form q(x1, x2,..., xn) = ∑i=1nxi2+∑1≤i≤j≤n(−1)j−ixixj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\s...
Published in Mathematische Zeitschrift
We present a definition of mutations of species with potential that can be applied to the species realizations of any skew-symmetrizable matrix B over cyclic Galois extensions E / F whose base field F has a primitive [E : F]th root of unity. After providing an example of a globally unfoldable skew-symmetrizable matrix whose species realizations do ...
Published in Forum Mathematicum
In this article, we give a definition and a classification of ‘higher’ simple-minded systems in triangulated categories generated by spherical objects with negative Calabi–Yau dimension. We also study mutations of this class of objects and that of ‘higher’ Hom-configurations and Riedtmann configurations. This gives an explicit analogue of the ‘nice...
Published in Frontiers of Mathematics in China
We consider whether the tilting properties of a tilting A-module T and a tilting B-module T′ can convey to their tensor product T ⊗ T′: The main result is that T ⊗ T′ turns out to be an (n + m)-tilting A ⊗ B-module, where T is an m-tilting A-module and T′ is an n-tilting B-module.
Published in Frontiers of Mathematics in China
We define the right regular dual of an object X in a monoidal category C; and give several results regarding the weak rigid monoidal category. Based on the definition of the right regular dual, we construct a weak Hopf algebra structure of H = End(F) whenever (F; J) is a fiber functor from category C to Vec and every X ∈ C has a right regular dual....
Published in Mathematische Zeitschrift
We call a 2-Calabi–Yau triangulated category a cluster category if its cluster-tilting subcategories form a cluster structure as defined in Buan et al. (Compos Math 145:1035–1079, 2009). In this paper, we show that the canonical orbit category of the bounded derived category of finite dimensional representations of a quiver without infinite paths o...
International audience
Published in Mathematische Zeitschrift
For a fixed finite dimensional algebra A, we study representation embeddings of the form mod(B)→mod(A)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$mod(B)\rightarrow ...
