Kawamata, Yujiro
Published in
Selecta Mathematica

We define a category of perverse coherent sheaves as the abelian category corresponding to the category of modules under Bondal–Rickard equivalence which arises from a tilting bundle for a projective morphism. The purpose of this paper is to determine versal non-commutative deformations of simple collections in the categories of perverse coherent s...

Hu, Yonggang Yao, Hailou
Published in
Results in Mathematics

In this paper, we introduce the notion of G-invariant recollements. Moreover, a series of examples of G-invariant recollements are provided. It is shown that each G-invariant recollement of derived categories of algebras induces that of skew group algebras. Applying this reuslt, we show that K-group decompositions and singularity equivalences can b...

Positselski, Leonid
Published in
Algebras and Representation Theory

We present the definition of a dedualizing complex of bicomodules over a pair of cocoherent coassociative coalgebras C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ma...

Dimitrov, George Katzarkov, Ludmil
Published in
Selecta Mathematica

In this paper we introduce new categorical notions and give many examples. In an earlier paper we proved that the Bridgeland stability space on the derived category of representations of K(l), the l-Kronecker quiver, is biholomorphic to C×H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amss...

Liu, Yu Zhe Zhang, Chao
Published in
Acta Mathematica Sinica, English Series

An algebra A is called derived-unique provided that any algebra which is derived equivalent to A is necessarily Morita equivalent to A. We classify derived-unique gentle algebras with at most one cycle using the combinatorial invariant introduced by Avella-Alaminos and Geiss.

Zhao, Zhibing Du, Xianneng Bao, Yanhong
Published in
Chinese Annals of Mathematics, Series B

Given a triangle functor F: A→B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{A}\rightarrow\mathcal{B}$$\end{document}, the authors introduce the half image h...

Hochenegger, Andreas Kalck, Martin Ploog, David
Published in
Mathematische Zeitschrift

We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality and the height of the poset. We explicitly describe spherical subcategories and their poset structure for derived categories of certain finite-dimensional algebras.

Gao, Nan Xu, Xiaojing
Published in
Chinese Annals of Mathematics, Series B

The aim of this paper is two-fold. Given a recollement (T′, T, T″, i*, i*, i!, j!, j*, j*), where T′, T, T″ are triangulated categories with small coproducts and T is compactly generated. First, the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i* preserves compact objects. As a con-sequence, gi...

Minamoto, Hiroyuki
Published in
European Journal of Mathematics

Even if a ring A is coherent, the polynomial ring A[X] in one variable could fail to be coherent. In this note we show that A[X] is graded coherent with the grading degX=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \...

Volkov, Yury Zvonareva, Alexandra
Published in
Algebras and Representation Theory

We generalize the notion of Külshammer ideals to the setting of a graded category. This allows us to define and study some properties of Külshammer type ideals in the graded center of a triangulated category and in the Hochschild cohomology of an algebra, providing new derived invariants. Further properties of Külshammer ideals are studied in the c...