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020 _a9783319098043
_9978-3-319-09804-3
024 7 _a10.1007/978-3-319-09804-3
_2doi
035 _ato000543901
040 _aSpringer
_cSpringer
_dRU-ToGU
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082 0 4 _a512.55
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082 0 4 _a512.482
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245 1 0 _aDevelopments and Retrospectives in Lie Theory
_helectronic resource
_bAlgebraic Methods /
_cedited by Geoffrey Mason, Ivan Penkov, Joseph A. Wolf.
260 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aX, 397 p. 85 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aDevelopments in Mathematics,
_x1389-2177 ;
_v38
505 0 _aGroup 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. Miličić) -- 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).
520 _aThis volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflectsthe 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 Algebraic 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 Algebraic Methods volume: Y. Bahturin, C. P. Bendel, B.D. Boe, J. Brundan, A. Chirvasitu, B. Cox, V. Dolgushev, C.M. Drupieski, M.G. Eastwood, V. Futorny, D. Grantcharov, A. van Groningen, M. Goze, J.-S. Huang, A.V. Isaev, I. Kashuba, R.A. Martins, G. Mason, D. Miličić, D.K., Nakano, S.-H. Ng, B.J. Parshall, I. Penkov, C. Pillen, E. Remm, V. Serganova, M.P. Tuite, H.D. Van, J.F. Willenbring, T. Willwacher, C.B. Wright, G. Yamskulna, G. Zuckerman.
650 0 _amathematics.
_9566183
650 0 _aGeometry, algebraic.
_9303684
650 0 _aTopological Groups.
_9305077
650 0 _aNumber theory.
_9566229
650 1 4 _aMathematics.
_9566184
650 2 4 _aTopological Groups, Lie Groups.
_9305078
650 2 4 _aAlgebraic Geometry.
_9303686
650 2 4 _aNumber Theory.
_9566230
700 1 _aMason, Geoffrey.
_eeditor.
_9451125
700 1 _aPenkov, Ivan.
_eeditor.
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700 1 _aWolf, Joseph A.
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710 2 _aSpringerLink (Online service)
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830 0 _aDevelopments in Mathematics,
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856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-09804-3
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