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Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.

Ordered algebraic structures --- Algebra --- Topological groups. Lie groups --- algebra --- wiskunde --- topologie

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Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profound contributions to mathematics. Due to Professor Wolf’s broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume.  Algebraic, geometric, and analytic methods are employed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representation spaces are discussed. Contributions in the area of representation theory involve numerous viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis.   Contributors   D. Akhiezer                         T. Oshima A. Andrada                         I. Pacharoni M. L. Barberis                    F. Ricci L. Barchini                            S. Rosenberg I. Dotti                                  N. Shimeno M. Eastwood                     J. Tirao V. Fischer                            S. Treneer T. Kobayashi                       C.T.C. Wall A. Korányi                           D. Wallace B. Kostant                           K. Wiboonton P. Kostelec                          F. Xu K.-H. Neeb                          O. Yakimova G. Olafsson                         R. Zierau B. Ørsted.

Lie groups. --- Harmonic analysis. --- Linear topological spaces. --- Symmetric spaces. --- Wolf, Joseph Albert, --- Lie algebras. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Topological Groups. --- Algebra. --- Functional analysis. --- Topological Groups, Lie Groups. --- Associative Rings and Algebras. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics --- Mathematical analysis --- Groups, Topological --- Continuous groups --- Topological groups. --- Associative rings. --- Rings (Algebra). --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Wolf, Joseph A.

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This volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those  workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics.  Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Geometric and Analytic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current research.  Most of the workshops have taken place at leading public and private universities in California, though on occasion workshops have taken place in Oregon, Louisiana and Utah.  Experts in representation theory/Lie theory from various parts of  the Americas, Europe and Asia have given talks at these meetings. The workshop series is robust, and the meetings continue on a quarterly basis.  Contributors to the Geometric and Analytic Methods volume: Y. Bahturin                                         D. Miličić P. Bieliavsky                                       K.-H. Neeb V. Gayral                                            G. Ólafsson A. de Goursac                                     E. Remm M. Goze                                             W. Soergel J. Hilgert                                             F. Spinnler A. Huckleberry                                    M. Yakimov T. Kobayashi                                       R. Zierau S. Mehdi  .

Lie algebras. --- Lie groups. --- Mathematics --- Research. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Mathematical research --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Topological Groups. --- Geometry, algebraic. --- Number theory. --- Topological Groups, Lie Groups. --- Algebraic Geometry. --- Number Theory. --- Mathematical Physics. --- Number study --- Numbers, Theory of --- Algebra --- Algebraic geometry --- Geometry --- Groups, Topological --- Continuous groups --- Topological groups. --- Algebraic geometry. --- Mathematical physics. --- Physical mathematics --- Physics

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Àlgebres de Lie --- Infinit --- Lie algebras. --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups

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Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profound contributions to mathematics. Due to Professor Wolf’s broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume.  Algebraic, geometric, and analytic methods are employed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representation spaces are discussed. Contributions in the area of representation theory involve numerous viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis.   Contributors   D. Akhiezer                         T. Oshima A. Andrada                         I. Pacharoni M. L. Barberis                    F. Ricci L. Barchini                            S. Rosenberg I. Dotti                                  N. Shimeno M. Eastwood                     J. Tirao V. Fischer                            S. Treneer T. Kobayashi                       C.T.C. Wall A. Korányi                           D. Wallace B. Kostant                           K. Wiboonton P. Kostelec                          F. Xu K.-H. Neeb                          O. Yakimova G. Olafsson                         R. Zierau B. Ørsted.

Mathematics --- Algebra --- Topological groups. Lie groups --- Functional analysis --- algebra --- topologie (wiskunde) --- functies (wiskunde) --- wiskunde