Derived equivalences and finite dimensional algebras

2006/03/15 by Raphaël Rouquier, Rouquier, Raphael · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0603356

openalex publication_date 2006/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry and categorifications.

Citations

• McKay equivalence for symplectic resolutions of singularities

Cited by

• Stable equivalences and homological dimensions
• The singularity category via the stabilization
• Derived equivalences, new matrix equivalences, and homological conjectures

Related

• Equivalences of derived categories for symmetric algebras
• Derived dimensions of representation-finite algebras
• Derived equivalences, restriction to self-injective subalgebras and invariance of homological dimensions
• Homotopes of finite-dimensional algebras
• Bounded derived categories and repetitive algebras