Ebook: Highlights in Lie Algebraic Methods
- Tags: Topological Groups Lie Groups, Category Theory Homological Algebra, General Algebraic Systems, Algebra, Linear and Multilinear Algebras Matrix Theory
- Series: Progress in Mathematics 295
- Year: 2012
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
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
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
Content:
Front Matter....Pages I-XV
Front Matter....Pages 1-1
Spherical Varieties....Pages 3-24
Consequences of the Littelmann Path Theory for the Structure of the Kashiwara B(?) Crystal....Pages 25-64
Structure and Representation Theory of Kac–Moody Superalgebras....Pages 65-102
Categories of Harish-Chandra Modules....Pages 103-122
Generalized Harish-Chandra Modules....Pages 123-143
Front Matter....Pages 145-145
B-Orbits of 2-Nilpotent Matrices and Generalizations....Pages 147-166
Weyl Denominator Identity for Finite-Dimensional Lie Superalgebras....Pages 167-188
Hopf Algebras and Frobenius Algebras in Finite Tensor Categories....Pages 189-203
Mutation Classes of 3?3 Generalized Cartan Matrices....Pages 205-211
Contractions and Polynomial Lie Algebras....Pages 213-227
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
Content:
Front Matter....Pages I-XV
Front Matter....Pages 1-1
Spherical Varieties....Pages 3-24
Consequences of the Littelmann Path Theory for the Structure of the Kashiwara B(?) Crystal....Pages 25-64
Structure and Representation Theory of Kac–Moody Superalgebras....Pages 65-102
Categories of Harish-Chandra Modules....Pages 103-122
Generalized Harish-Chandra Modules....Pages 123-143
Front Matter....Pages 145-145
B-Orbits of 2-Nilpotent Matrices and Generalizations....Pages 147-166
Weyl Denominator Identity for Finite-Dimensional Lie Superalgebras....Pages 167-188
Hopf Algebras and Frobenius Algebras in Finite Tensor Categories....Pages 189-203
Mutation Classes of 3?3 Generalized Cartan Matrices....Pages 205-211
Contractions and Polynomial Lie Algebras....Pages 213-227
....