3 citations · 11 across the 7 of their papers we have counts for
7 papers
On -exact categories I: The existence and uniqueness of maximal -exact structures
Carlo Klapproth
This paper is the first part of a series that investigates the existence of -exact structures on idempotent complete additive categories for positive integers . It is shown t…
Obstructions to semiorthogonal decompositions for singular projective varieties II: Representation theory
Martin Kalck, Carlo Klapproth, Nebojsa Pavic
We show that odd-dimensional projective varieties with tilting objects and only ADE-hypersurface singularities are nodal, i.e. they only have -singularities. This is a very sp…
-Extension closed subcategories of -exangulated categories
Carlo Klapproth
Let be a positive integer. We show that an -extension closed subcategory of an -exangulated category naturally inherits an -exangulated structure through restriction o…
Idempotent completions of -exangulated categories
Carlo Klapproth, Dixy Msapato, Amit Shah
Suppose is an -exangulated category. We show that the idempotent completion and the weak idempotent completion of are again…
When does the Auslander-Reiten translation operate linearly on the Grothendieck group? -- Part I
Carlo Klapproth
For a hereditary, finite-dimensional algebra the Coxeter transformation extends the action of the Auslander--Reiten translation on the non-projective indecomposable modules to…
A method for constructing minimal projective resolutions over idempotent subrings
Carlo Klapproth
We show how to obtain minimal projective resolutions of finitely generated modules over an idempotent subring of a semiperfect noetherian basic ring by a c…
-Exact categories arising from -angulated categories
Carlo Klapproth
Let be an -angulated Krull-Schmidt category and an -extension closed, additive and full subcategory with $\operatorname{Ho…