# The Derived Equivalence Classification of Representation-Finite Selfinjective Algebras

@article{Asashiba1999TheDE, title={The Derived Equivalence Classification of Representation-Finite Selfinjective Algebras}, author={Hideto Asashiba}, journal={Journal of Algebra}, year={1999}, volume={214}, pages={182-221} }

## 98 Citations

DERIVED EQUIVALENCES FOR Φ-AUSLANDER-YONEDA ALGEBRAS

- Mathematics
- 2013

In this paper, we first define a new family of Yoneda algebras, called Φ-Auslander-Yoneda algebras, in triangulated categories by introducing the notion of admissible sets Φ in N, which includes…

Indecomposable Calabi-Yau objects in stable module categories of finite type

- Mathematics
- 2011

The authors give a discription of the stable categories of selfinjective algebras of finite representation type over an algebraically closed field, which admits indecomposable Calabi-Yau obdjects.…

Derived Picard groups of symmetric representation-finite algebras of type $D$

- Mathematics
- 2021

We explicitly describe the derived Picard groups of symmetric representation-finite algebras of type D. In particular, we prove that these groups are generated by spherical twists along collections…

From groups to clusters

- Mathematics
- 2016

We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their…

Derived equivalences, restriction to self-injective subalgebras and invariance of homological dimensions

- Mathematics
- 2016

Derived equivalences between finite dimensional algebras do, in general, not pass to centraliser (or other) subalgebras, nor do they preserve homological invariants of the algebras, such as global or…

Realizing orbit categories as stable module categories: a complete classification

- Mathematics
- 2015

We classify all triangulated orbit categories of path-algebras of Dynkin diagrams that are triangle equivalent to a stable module category of a representation-finite self-injective standard algebra.…

Tilting Mutation of Weakly Symmetric Algebras and Stable Equivalence

- Mathematics
- 2014

We consider tilting mutations of a weakly symmetric algebra at a subset of simple modules, as recently introduced by T. Aihara. These mutations are defined as the endomorphism rings of certain…

Álgebras de malla finito dimensionales y sus propiedades homológicas= Finite dimensional mesh algebras and their homological properties.

- Mathematics
- 2013

Resumen Esta Tesis Doctoral esta enmarcada dentro del area del Algebra, concretamente, de la Teoria de Representacion de Algebras. El objetivo principal de la misma es el estudio de propiedades…

A combinatorial classification of thick subcategories of derived and stable categories

- Mathematics
- 2011

In this thesis, we investigate thick subcategories for stable categories of certain Frobenius categories and for derived categories of hereditary abelian categories. Both types of categories arise in…

Derived equivalences for $\Phi$-Auslander-Yoneda algebras

- Mathematics
- 2009

In this paper, we introduce $\Phi$-Auslander-Yoneda algebras in a triangulated category with $\Phi$ a parameter set in $\mathbb N$, and provide a method to construct new derived equivalences between…

## References

SHOWING 1-10 OF 17 REFERENCES

Selfinjective and simply connected algebras

- Mathematics
- 1981

In this paper, we present a new approach to the problem of classifying all basic finite-dimensional algebras over an algebraically closed field k which are connected, selfinjective and…