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Derived equivalences of algebras
Author(s) -
Xi Changchang
Publication year - 2018
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12209
Subject(s) - mathematics , conjecture , homological algebra , pure mathematics , abelian group , representation theory , global dimension , algebra over a field , dimension (graph theory) , algebraic number , algebraic geometry , mathematical analysis , functor
Derived categories and equivalences between them are the pièce de résistance of modern homological algebra. They are widely used in many branches of mathematics, especially in algebraic geometry and representation theory. In this note, we shall survey some recently developed construction methods of derived equivalences for algebras and rings, with applications to homological conjectures, such as Broué's abelian defect group conjecture and the finitistic dimension conjecture, and to computation of higher algebraic K ‐groups of algebras and rings.