Ebook: Developments and Trends in Infinite-Dimensional Lie Theory
- Tags: Topological Groups Lie Groups, Group Theory and Generalizations, Algebra, Geometry, Algebraic Geometry
- Series: Progress in Mathematics 288
- Year: 2011
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups.
Part (A) is mainly concerned with the structure and representation theory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac–Moody superalgebras.
The articles in Part (B) examine connections between infinite-dimensional Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordan-theoretic geometries and new results on direct-limit groups.
The analytic representation theory of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach–Lie–Poisson spaces, and infinite-dimensional generalizations of reductive Lie groups.
Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.
This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups.
Part (A) is mainly concerned with the structure and representation theory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac–Moody superalgebras.
The articles in Part (B) examine connections between infinite-dimensional Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordan-theoretic geometries and new results on direct-limit groups.
The analytic representation theory of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach–Lie–Poisson spaces, and infinite-dimensional generalizations of reductive Lie groups.
Contributors: B. Allison, D. Belti??, W. Bertram, J. Faulkner, Ph. Gille, H. Gl?ckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.
This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups.
Part (A) is mainly concerned with the structure and representation theory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac–Moody superalgebras.
The articles in Part (B) examine connections between infinite-dimensional Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordan-theoretic geometries and new results on direct-limit groups.
The analytic representation theory of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach–Lie–Poisson spaces, and infinite-dimensional generalizations of reductive Lie groups.
Contributors: B. Allison, D. Belti??, W. Bertram, J. Faulkner, Ph. Gille, H. Gl?ckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.
Content:
Front Matter....Pages i-viii
Front Matter....Pages 1-1
Isotopy for Extended Affine Lie Algebras and Lie Tori....Pages 3-43
Remarks on the Isotriviality of Multiloop Algebras....Pages 45-51
Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras – A Survey....Pages 53-126
Tensor Representations of Classical Locally Finite Lie Algebras....Pages 127-150
Lie Algebras, Vertex Algebras, and Automorphic Forms....Pages 151-168
Kac–Moody Superalgebras and Integrability....Pages 169-218
Front Matter....Pages 219-219
Jordan Structures and Non-Associative Geometry....Pages 221-241
Direct Limits of Infinite-Dimensional Lie Groups....Pages 243-280
Lie Groups of Bundle Automorphisms and Their Extensions....Pages 281-338
Gerbes and Lie Groups....Pages 339-364
Front Matter....Pages 365-365
Functional Analytic Background for a Theory of Infinite-Dimensional Reductive Lie Groups....Pages 367-392
Heat Kernel Measures and Critical Limits....Pages 393-415
Coadjoint Orbits and the Beginnings of a Geometric Representation Theory....Pages 417-457
Infinite-Dimensional Multiplicity-Free Spaces I: Limits of Compact Commutative Spaces....Pages 459-481
Back Matter....Pages 483-492
This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups.
Part (A) is mainly concerned with the structure and representation theory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac–Moody superalgebras.
The articles in Part (B) examine connections between infinite-dimensional Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordan-theoretic geometries and new results on direct-limit groups.
The analytic representation theory of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach–Lie–Poisson spaces, and infinite-dimensional generalizations of reductive Lie groups.
Contributors: B. Allison, D. Belti??, W. Bertram, J. Faulkner, Ph. Gille, H. Gl?ckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.
Content:
Front Matter....Pages i-viii
Front Matter....Pages 1-1
Isotopy for Extended Affine Lie Algebras and Lie Tori....Pages 3-43
Remarks on the Isotriviality of Multiloop Algebras....Pages 45-51
Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras – A Survey....Pages 53-126
Tensor Representations of Classical Locally Finite Lie Algebras....Pages 127-150
Lie Algebras, Vertex Algebras, and Automorphic Forms....Pages 151-168
Kac–Moody Superalgebras and Integrability....Pages 169-218
Front Matter....Pages 219-219
Jordan Structures and Non-Associative Geometry....Pages 221-241
Direct Limits of Infinite-Dimensional Lie Groups....Pages 243-280
Lie Groups of Bundle Automorphisms and Their Extensions....Pages 281-338
Gerbes and Lie Groups....Pages 339-364
Front Matter....Pages 365-365
Functional Analytic Background for a Theory of Infinite-Dimensional Reductive Lie Groups....Pages 367-392
Heat Kernel Measures and Critical Limits....Pages 393-415
Coadjoint Orbits and the Beginnings of a Geometric Representation Theory....Pages 417-457
Infinite-Dimensional Multiplicity-Free Spaces I: Limits of Compact Commutative Spaces....Pages 459-481
Back Matter....Pages 483-492
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