Relative Derived Categories

2021 ◽  
Author(s):  
Yanping Liu
Keyword(s):  
Derived Categories

scholarly journals Curved Rickard complexes and link homologies

2020 ◽  
Vol 2020 (769) ◽  
pp. 87-119
Author(s):  
Sabin Cautis ◽  
Aaron D. Lauda ◽  
Joshua Sussan
Keyword(s):  
Spectral Sequence ◽  
Quantum Groups ◽  
Braid Group ◽  
Derived Categories ◽  
Duke Math ◽  
Khovanov Homology ◽  
Hilbert Schemes ◽  
Coherent Sheaves ◽  
Knot Homology ◽  
Original Motivation

AbstractRickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to obtain deformations of link homologies which generalize those of Batson–Seed [3] [J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 2015, 5, 801–841] and Gorsky–Hogancamp [E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint 2017] to arbitrary representations/partitions. Another is to relate the deformed homology defined algebro-geometrically in [S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, colored links, Quantum Topol. 8 2017, 2, 381–411] to categorified quantum groups (this was the original motivation for this paper).

Finiteness conditions and relative derived categories

2021 ◽  
Vol 573 ◽  
pp. 270-296
Author(s):  
Lingling Tan ◽  
Dingguo Wang ◽  
Tiwei Zhao
Keyword(s):  
Derived Categories ◽  
Finiteness Conditions

scholarly journals Hilbert squares: derived categories and deformations

2019 ◽  
Vol 25 (3) ◽  
Author(s):  
Pieter Belmans ◽  
Lie Fu ◽  
Theo Raedschelders
Keyword(s):  
Derived Categories

Piecewise Hereditary Triangular Matrix Algebras

2021 ◽  
Vol 28 (01) ◽  
pp. 143-154
Author(s):  
Yiyu Li ◽  
Ming Lu
Keyword(s):  
Positive Integer ◽  
Triangular Matrix ◽  
Derived Categories ◽  
Matrix Algebras ◽  
Tensor Algebras ◽  
Finite Dimensional ◽  
Abelian Categories ◽  
Upper Triangular Matrix ◽  
Orbit Categories ◽  
Finite Dimensional Algebras

For any positive integer [Formula: see text], we clearly describe all finite-dimensional algebras [Formula: see text] such that the upper triangular matrix algebras [Formula: see text] are piecewise hereditary. Consequently, we describe all finite-dimensional algebras [Formula: see text] such that their derived categories of [Formula: see text]-complexes are triangulated equivalent to derived categories of hereditary abelian categories, and we describe the tensor algebras [Formula: see text] for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories.

scholarly journals Cohomology of groups and splendid equivalences of derived categories

2001 ◽  
Vol 131 (3) ◽  
pp. 459-472 ◽  
Author(s):  
ALEXANDER ZIMMERMANN
Keyword(s):  
Group Ring ◽  
Local Structure ◽  
Cohomology Ring ◽  
Derived Categories ◽  
Derived Category ◽  
Restriction Map ◽  
Group Rings ◽  
Cohomology Rings ◽  
The Impact ◽  
Cohomology Of Groups

In an earlier paper we studied the impact of equivalences between derived categories of group rings on their cohomology rings. Especially the group of auto-equivalences TrPic(RG) of the derived category of a group ring RG as introduced by Raphaël Rouquier and the author defines an action on the cohomology ring of this group. We study this action with respect to the restriction map, transfer, conjugation and the local structure of the group G.

scholarly journals Derived categories, tilted algebras, and Drinfel'd doubles

2003 ◽  
Vol 266 (2) ◽  
pp. 723-748 ◽  
Author(s):  
Liangang Peng ◽  
Youjun Tan
Keyword(s):  
Derived Categories ◽  
Tilted Algebras ◽  
Drinfel'd Doubles

scholarly journals Traits and values as predictors of the frequency of everyday behavior: Comparison between models and levels

2018 ◽  
Vol 40 (1) ◽  
pp. 133-153 ◽  
Author(s):  
Ewa Skimina ◽  
Jan Cieciuch ◽  
Włodzimierz Strus
Keyword(s):  
Personality Traits ◽  
Factor Model ◽  
Five Factor Model ◽  
Personal Values ◽  
Derived Categories ◽  
Higher Order ◽  
Behavioral Factors ◽  
Wide Range ◽  
Age Range ◽  
Hexaco Model

AbstractThe aims of this study were to compare (a) personality traits vs personal values, (b) Five-Factor Model (FFM) vs HEXACO model of personality traits, and (c) broad vs narrow personality constructs in terms of their relationship with the frequency of everyday behaviors. These relationships were analyzed at three organizational levels of self-reported behavior: (a) single behavioral acts, (b) behavioral components (empirically derived categories of similar behaviors), and (c) two higher-order factors. The study was conducted on a Polish sample (N = 532, age range 16–72). We found that (a) even the frequencies of single behavioral acts were related to various personality constructs instead of one narrow trait or value, (b) personality traits and personal values were comparable as predictors of a wide range of everyday behaviors, (c) HEXACO correlated with the frequency of behaviors slightly higher than FFM, and (d) narrow and broad personality constructs did not differ substantially as predictors of everyday behavior at the levels of acts and components, but at the level of higher-order behavioral factors, broad personality measures were better predictors than narrow ones.

Sign in / Sign up

Export Citation Format

Share Document