An outgrowth of a two-week summer session at Jacobs University in Bremen, Germany in August 2009 ("Structures in Lie Theory, Crystals, Derived Functors, Harish-Chandra Modules, Invariants and Quivers"), this volume consists of expository and research articles that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and Kac-Moody Lie algebras, modular representations, primitive ideals, representation theory of Artin algebras and quivers, Kac-Moody superalgebras, categories of Harish-Chandra modules, cohomological methods, and cluster algebras.

List of Contributors:

M. Boos

M. Brion

J. Fuchs

M. Gorelik

A. Joseph

M. Reineke

C. Schweigert

V. Serganova

A. Seven

W. Soergel

B. Wilson

G. Zuckerman

Zusammenfassung
This volume consists of expository and research articles that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and KacMoody Lie algebras, modular representations, primitive ideals, representation theory of Artin algebras and quivers, KacMoody superalgebras, categories of HarishChandra modules, cohomological methods, and cluster algebras.

Inhalt
Preface.- Part I: The Courses.- 1 Spherical Varieties.- 2 Consequences of the Littelmann Path Model for the Structure of the Kashiwara B() Crystal.- 3 Structure and Representation Theory of KacMoody Superalgebras.- 4 Categories of HarishChandra Modules.- 5 Generalized HarishChandra Modules.- Part II: The Papers.- 6 B-Orbits of 2-Nilpotent Matrices.- 7 The Weyl Denominator Identity for Finite-Dimensional Lie Superalgebras.- 8 Hopf Algebras and Frobenius Algebras in Finite Tensor Categories.- 9 Mutation Classes of 3 x 3 Generalized Cartan Matrices.- 10 Contractions and Polynomial Lie Algebras.