Developments and Retrospectives in Lie Theory

Algebraic Methods

Geoffrey Mason, Ivan Penkov, Joseph A. Wolf (Herausgeber)

Buch | Softcover

X, 397 Seiten

2016 | 1. Softcover reprint of the original 1st ed. 2014
Springer International Publishing (Verlag)
978-3-319-37820-6 (ISBN)

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The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. These workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. At the beginning, the top universities in California and Utah hosted the meetings which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. The contributors to this volume have all participated in these Lie theory workshops and include in this volume expository articles which cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned-above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

Group gradings on Lie algebras with applications to geometry. I (Y. Bahturin, M. Goze, E. Remm).- Bounding the dimensions of rational cohomology groups (C.P. Bendel, B.D. Boe, C.M. Drupieski, D.K. Nakano, B.J. Parshall, C. Pillen, C.B. Wright).- Representations of the general linear Lie superalgebra in the BGG Category {$/mathcal O$} (J. Brundan).- Three results on representations of Mackey Lie algebras (A. Chirvasitu).- Free field realizations of the Date-Jimbo-Kashiwara-Miwa algebra (B. Cox, V. Futorny, R.A. Martins).- The deformation complex is a homotopy invariant of a homotopy algebra (V. Dolgushev, T. Willwacher).- Invariants of Artinian Gorenstein algebras and isolated hypersurface singularities (M.G. Eastwood, A.V. Isaev).- Generalized loop modules for affine Kac-Moody algebras (V. Futorny, I. Kashuba).- Twisted localization of weight modules (D. Grantcharov).- Dirac cohomology and generalization of classical branching rules (J.-S. Huang).- Cleft extensions and quotients of twisted quantum doubles (G. Mason, S.-H. Ng).- On the structure of ${/Bbb N}$-graded vertex operator algebras (G. Mason, G. Yamskulna).- Variations on a Casselman-Osborne theme (D. Milicic).- Tensor representations of Mackey Lie algebras and their dense subalgebras (I. Penkov, V. Serganova).- Algebraic methods in the theory of generalized Harish-Chandra modules (I. Penkov, G. Zuckerman).- On exceptional vertex operator (super) algebras (M.P. Tuite, H.D. Van).- The cubic, the quartic, and the exceptional group $G_2$ (A. van Groningen, J.F. Willenbring).

Erscheinungsdatum	16.09.2016
Reihe/Serie	Developments in Mathematics
Zusatzinfo	X, 397 p. 85 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebraic Geometry • Differential Geometry • Groups and group theory • Harmonic Analysis • Kazhdan-Lusztig conjectures • Mathematical Physics • Mathematics • mathematics and statistics • Number Theory • Representation Theory • superalgebras • Topological Groups, Lie Groups
ISBN-10	3-319-37820-1 / 3319378201
ISBN-13	978-3-319-37820-6 / 9783319378206
Zustand	Neuware