Derived equivalences and finite dimensional algebras

By Raphaël Rouquier. 2006

79 citations recorded by the source corpus.

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

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4d91f14c522735322d7865f8353145214af751ba

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A categorification of quantum sl(n) (2008, background): “Another connection worth mentioning is the relationship to Chuang and Rouquier’s sl2 categorifications [12] (see also [39]).”
Derived equivalences and stable equivalences of Morita type, I (2008, background): “To be able to lift stable equivalences of Morita type to derived equivalences is important for instance in one approach, due to Rouquier [48], to Broué’s abelian defect group conjecture.”
Representation theory of symmetric groups and related Hecke algebras (2009, unknown): “The affine Khovanov-Lauda-Rouquier algebras were introduced independently by Khovanov-Lauda [113, 114] and Rouquier [174].”
The Hodge theory of Soergel bimodules (2012, background): “We feel it is justiﬁed in our setting because it was Rouquier who ﬁrst emphasised that concrete algebraic properties of these complexes should have applications for arbitrary Coxeter systems [Rou06b, 4.2.1].”