König, Steffen.
Derived Equivalences for Group Rings [electronic resource] / by Steffen König, Alexander Zimmermann. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1998. - X, 246 p. online resource. - Lecture Notes in Mathematics, 1685 0075-8434 ; . - Lecture Notes in Mathematics, 1685 .
Basic definitions and some examples -- Rickard's fundamental theorem -- Some modular and local representation theory -- Onesided tilting complexes for group rings -- Tilting with additional structure: twosided tilting complexes -- Historical remarks -- On the construction of triangle equivalences -- Triangulated categories in the modular representation theory of finite groups -- The derived category of blocks with cyclic defect groups -- On stable equivalences of Morita type.
A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.
9783540697480
10.1007/BFb0096366 doi
Mathematics.
Group theory.
K-theory.
Mathematics.
Group Theory and Generalizations.
K-Theory.
QA174-183
512.2
Derived Equivalences for Group Rings [electronic resource] / by Steffen König, Alexander Zimmermann. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1998. - X, 246 p. online resource. - Lecture Notes in Mathematics, 1685 0075-8434 ; . - Lecture Notes in Mathematics, 1685 .
Basic definitions and some examples -- Rickard's fundamental theorem -- Some modular and local representation theory -- Onesided tilting complexes for group rings -- Tilting with additional structure: twosided tilting complexes -- Historical remarks -- On the construction of triangle equivalences -- Triangulated categories in the modular representation theory of finite groups -- The derived category of blocks with cyclic defect groups -- On stable equivalences of Morita type.
A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.
9783540697480
10.1007/BFb0096366 doi
Mathematics.
Group theory.
K-theory.
Mathematics.
Group Theory and Generalizations.
K-Theory.
QA174-183
512.2