Silting objects
L Angeleri Hügel - Bulletin of the London Mathematical Society, 2019 - Wiley Online Library
We give an overview of recent developments in silting theory. After an introduction on torsion
pairs in triangulated categories, we discuss and compare different notions of silting and …
pairs in triangulated categories, we discuss and compare different notions of silting and …
[HTML][HTML] Cosilting complexes and AIR-cotilting modules
P Zhang, J Wei - Journal of Algebra, 2017 - Elsevier
We introduce and study the new concepts of cosilting complexes, cosilting modules and AIR-
cotilting modules. We prove that the three concepts AIR-cotilting modules, cosilting modules …
cotilting modules. We prove that the three concepts AIR-cotilting modules, cosilting modules …
[HTML][HTML] A silting theorem
We give a generalization of the classical tilting theorem of Brenner and Butler. We show that
for a 2-term silting complex P in the bounded homotopy category K b (proj A) of finitely …
for a 2-term silting complex P in the bounded homotopy category K b (proj A) of finitely …
On the abundance of silting modules
LA Hügel - Surveys in Representation Theory of Algebras” …, 2018 - books.google.com
Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a
noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also …
noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also …
[HTML][HTML] Derived equivalences via HRS-tilting
Let A be an abelian category and B be the Happel-Reiten-Smalø tilt of A with respect to a
torsion pair. We give necessary and sufficient conditions for the existence of a derived …
torsion pair. We give necessary and sufficient conditions for the existence of a derived …
Endomorphism algebras of 2-term silting complexes
We study possible values of the global dimension of endomorphism algebras of 2-term
silting complexes. We show that for any algebra A whose global dimension gl. dim A≤ 2 …
silting complexes. We show that for any algebra A whose global dimension gl. dim A≤ 2 …
[PDF][PDF] There are no strictly shod algebras in hereditary gentle algebras
H Zhang, YZ Liu - arXiv preprint arXiv:2212.09105, 2022 - arxiv.org
arXiv:2212.09105v1 [math.RT] 18 Dec 2022 Page 1 arXiv:2212.09105v1 [math.RT] 18 Dec
2022 THERE ARE NO STRICTLY SHOD ALGEBRAS IN HEREDITARY GENTLE ALGEBRAS …
2022 THERE ARE NO STRICTLY SHOD ALGEBRAS IN HEREDITARY GENTLE ALGEBRAS …
Self-orthogonal τ-tilting modules and tilting modules
X Zhang - Journal of Pure and Applied Algebra, 2022 - Elsevier
Let Λ be an Artin algebra and T a τ-tilting Λ-module. We prove that T is a tilting module if and
only if Ext Λ i (T, Fac T)= 0 for all i≥ 1, where Fac T is the full subcategory consisting of …
only if Ext Λ i (T, Fac T)= 0 for all i≥ 1, where Fac T is the full subcategory consisting of …
[PDF][PDF] Nakayama algebras of small homological dimension and pattern avoiding permutations
V Klász, R Marczinzik, J Marquardt - arXiv preprint arXiv:2403.11359, 2024 - arxiv.org
arXiv:2403.11359v1 [math.RT] 17 Mar 2024 Page 1 NAKAYAMA ALGEBRAS OF SMALL
HOMOLOGICAL DIMENSION AND PATTERN AVOIDING PERMUTATIONS VIKT ORIA KL ÁSZ1 …
HOMOLOGICAL DIMENSION AND PATTERN AVOIDING PERMUTATIONS VIKT ORIA KL ÁSZ1 …
The representation invariants of 2-term silting complexes
Y Hu - Communications in Algebra, 2021 - Taylor & Francis
Let A be a finite dimensional k-algebra and P a 2-term silting complex in K b (proj A). In this
article, we investigate the representation dimension of End D b (A)(P) by the silting theory …
article, we investigate the representation dimension of End D b (A)(P) by the silting theory …