# Derived and Stable Equivalence Classification of Twisted Multifold Extensions of Piecewise Hereditary Algebras of Tree Type

@article{Asashiba2002DerivedAS, title={Derived and Stable Equivalence Classification of Twisted Multifold Extensions of Piecewise Hereditary Algebras of Tree Type}, author={Hideto Asashiba}, journal={Journal of Algebra}, year={2002}, volume={249}, pages={345-376} }

## 14 Citations

Invariance of selfinjective algebras of quasitilted type under stable equivalences

- Mathematics
- 2006

We prove that the class of finite dimensional selfinjective algebras over a field which admit Galois coverings by the repetitive algebras of the quasitilted algebras, with Galois groups generated by…

Gluing of derived equivalences of dg categories

- Mathematics
- 2022

A diagram consisting of differential graded (dg for short) categories and dg functors is formutated as a colax functor X from a small category I to the 2category k-dgCat of dg categories, dg functors…

Cohen–Montgomery Duality for Pseudo-actions of a Group

- Mathematics
- 2020

Throughout this article, we fix a group G and a commutative ring
$$\Bbbk $$
. This is an exposition on 2-equivalences between a 2-category of small
$$\Bbbk $$
-categories with pseudo G-actions…

Smash products of group weighted bound quivers and Brauer graphs

- MathematicsCommunications in Algebra
- 2019

Abstract Let be a field, G a group, and (Q, I) a bound quiver. A map is called a G-weight on Q, which defines a G-graded -category , and W is called homogeneous if I is a homogeneous ideal of the…

Gorenstein versions of covering techniques for linear categories and their applications

- MathematicsJournal of Algebra
- 2018

On isomorphisms of generalized multifold extensions of algebras without nonzero oriented cycles

- Mathematics
- 2018

Abstract Assume that a basic algebra A over an algebraically closed field with a basic set A 0 of primitive idempotents has the property that for all Let n be a nonzero integer, and and two…

Derived equivalence classification of generalized multifold extensions of piecewise hereditary algebras of tree type

- Mathematics
- 2015

We give a derived equivalence classification of algebras of the form \(\hat{A}/\ang{\ph}\) for some piecewise hereditary algebra \(A\) of tree type and some automorphism \(\ph\) of \(\hat{A}\) such…

Derived Equivalences of Actions of a Category

- MathematicsAppl. Categorical Struct.
- 2013

This work investigates derived equivalences of those oplax functors, and establishes a Morita type theorem for them, which gives a base of investigations of derived equivalence of Grothendieck constructions of those Oplaxfunctors.

## References

SHOWING 1-10 OF 20 REFERENCES

The Derived Equivalence Classification of Representation-Finite Selfinjective Algebras

- Mathematics
- 1999

Stable equivalence of selfinjective algebras of tilted type

- Mathematics
- 1998

Abstract. A finite dimensional K-algebra
$\it\Lambda $ is called selfinjective of tilted type if
$\it\Lambda $ is a quotient
$\widehat {B}/(\varphi \nu _{\hat {B}})$, where
$\widehat {B}$ is the…

Deriving DG categories

- Mathematics
- 1994

— We investigate the (unbounded) derived category of a differential Z-graded category (=DG category). As a first application, we deduce a "triangulated analogue" (4.3) of a theorem of Freyd's [5],…

Representations of Finite-Dimensional Algebras

- Mathematics
- 1992

1. Matrix Problems.- 2. Algebras, Modules and Categories.- 3. Radical, Decomposition, Aggregates.- 4. Finitely Spaced Modules.- 5. Finitely Represented Posets.- 6. Roots.- 7. Representations of…

Isométrie parfaites , types de blocs , catégories dérivées

- Astérisque
- 1990

Isométrie parfaites, types de blocs, catégories dérivées, Astérisque

- 1990