Equivalences of derived categories for symmetric algebras

By J. Rickard. 2002

97 citations recorded by the source corpus.

We give a characterization of the sets of objects of the derived category of a block of a finite group algebra (or other symmetric algebra) that occur as the set of images of simple modules under an equivalence of derived categories. We give some applications to proving that certain blocks have equivalent derived categories.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f9a2685d39f0b166e52325110b3b28619c68603c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Changchang Xi
2. Dong Ping Yang
3. Yuming Liu
4. S. Koenig
5. Osamu Iyama
6. Jiaqun Wei
7. B. Keller
8. Pierre-Guy Plamondon

In Geometry and Topology

1. Changchang Xi
2. S. Koenig
3. Dong Ping Yang
4. Yuming Liu
5. Osamu Iyama
6. Jiaqun Wei
7. B. Keller
8. Yuya Mizuno

In Statistical and Nonlinear Physics

1. Dong Ping Yang
2. Yuming Liu
3. S. Koenig
4. Changchang Xi
5. Sotaro Asai
6. Yuya Mizuno
7. Osamu Iyama

Citations in the corpus

• Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras (2012, methodology): “We will construct a silting object ν−1T of Kb(projΛ) following a method of Rickard [43].”
• Constructions of stable equivalences of Morita type for finite‐dimensional algebras III (2007, methodology): “It has been used to study blocks in the representation theory of finite groups, or more generally, finite-dimensional self-injective algebras [14, 20, 21].”