LEADER 06010nam 22007215 450 001 9910299968403321 005 20200701162332.0 010 $a3-319-09804-7 024 7 $a10.1007/978-3-319-09804-3 035 $a(CKB)3710000000269882 035 $a(EBL)1968031 035 $a(SSID)ssj0001372586 035 $a(PQKBManifestationID)11734863 035 $a(PQKBTitleCode)TC0001372586 035 $a(PQKBWorkID)11310454 035 $a(PQKB)10160795 035 $a(MiAaPQ)EBC1968031 035 $a(DE-He213)978-3-319-09804-3 035 $a(PPN)182098184 035 $a(EXLCZ)993710000000269882 100 $a20141031d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDevelopments and Retrospectives in Lie Theory $eAlgebraic Methods /$fedited by Geoffrey Mason, Ivan Penkov, Joseph A. Wolf 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (403 p.) 225 1 $aDevelopments in Mathematics,$x1389-2177 ;$v38 300 $aDescription based upon print version of record. 311 $a3-319-09803-9 320 $aIncludes bibliographical references. 327 $aGroup gradings on Lie algebras with applications to geometry. I (Y. Bahturin, M. Goze, E. Remm) -- Bounding the dimensions of rational cohomology groups (C.P. Bendel, B.D. Boe, C.M. Drupieski, D.K. Nakano, B.J. Parshall, C. Pillen, C.B. Wright) -- Representations of the general linear Lie superalgebra in the BGG Category {$\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. Mili?i?) -- 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). 330 $aThis volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those  workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics.  Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Algebraic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current research.  Most of the workshops have taken place at leading public and private universities in California, though on occasion workshops have taken place in Oregon, Louisiana and Utah.  Experts in representation theory/Lie theory from various parts of  the Americas, Europe and Asia have given talks at these meetings. The workshop series is robust, and the meetings continue on a quarterly basis.  Contributors to the Algebraic Methods volume: Y. Bahturin, C. P. Bendel, B.D. Boe, J. Brundan, A. Chirvasitu, B. Cox, V. Dolgushev, C.M. Drupieski, M.G. Eastwood, V. Futorny, D. Grantcharov, A. van Groningen, M. Goze, J.-S. Huang, A.V. Isaev, I. Kashuba, R.A. Martins, G. Mason, D. Mili?i?, D.K., Nakano, S.-H. Ng, B.J. Parshall, I. Penkov, C. Pillen, E. Remm, V. Serganova, M.P. Tuite, H.D. Van, J.F. Willenbring, T. Willwacher, C.B. Wright, G. Yamskulna, G. Zuckerman. 410 0$aDevelopments in Mathematics,$x1389-2177 ;$v38 606 $aTopological groups 606 $aLie groups 606 $aGeometry, Algebraic 606 $aNumber theory 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aTopological groups. 615 0$aLie groups. 615 0$aGeometry, Algebraic. 615 0$aNumber theory. 615 14$aTopological Groups, Lie Groups. 615 24$aAlgebraic Geometry. 615 24$aNumber Theory. 676 $a510 676 $a512.55 676 $a512.7 676 $a512482 676 $a516.35 702 $aMason$b Geoffrey$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aPenkov$b Ivan$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aWolf$b Joseph A$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910299968403321 996 $aDevelopments and retrospectives in Lie theory$91409894 997 $aUNINA