LEADER 04741nam 22006613 450 001 9910957044903321 005 20231110230541.0 010 $a9781470465285 010 $a1470465280 035 $a(CKB)4100000011975358 035 $a(MiAaPQ)EBC6661105 035 $a(Au-PeEL)EBL6661105 035 $a(OCoLC)1259594040 035 $a(RPAM)22488172 035 $a(EXLCZ)994100000011975358 100 $a20210901d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCohomological Tensor Functors on Representations of the General Linear Supergroup 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$dİ2021. 215 $a1 online resource (118 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.270 311 08$a9781470447144 311 08$a1470447142 320 $aIncludes bibliographical references. 327 $aCover -- Title page -- Chapter 1. Introduction -- Chapter 2. Cohomological Tensor Functors -- 2.1. The superlinear groups -- 2.2. The Duflo-Serganova functor -- 2.3. Cohomology functors -- 2.4. Support varieties and the kernel of -- 2.5. The tensor functor -- 2.6. The relation between ( ) and ( ) -- 2.7. Hodge decomposition -- 2.8. The case > -- 1 -- 2.9. Boundary maps -- 2.10. Highest weight modules -- 2.11. The Casimir -- Chapter 3. The Main Theorem and its Proof -- 3.1. The language of Brundan and Stroppel -- 3.2. On segments, sectors and plots -- 3.3. Mixed tensors and ground states -- 3.4. Sign normalizations -- 3.5. The main theorem -- 3.6. Strategy of the proof -- 3.7. Modules of Loewy length 3 -- 3.8. Inductive Control over -- 3.9. Moves -- Chapter 4. Consequences of the Main Theorem -- 4.1. Tannaka Duals -- 4.2. Cohomology I -- 4.3. Cohomology II -- 4.4. Cohomology III -- 4.5. The forest formula -- 4.6. -module structure on the cohomology ^{?}_{ _{ }} -- 4.7. Primitive elements of ^{?}_{ _{ }}( (1)) -- 4.8. Kac module of 1 -- 4.9. Strict morphisms -- 4.10. The module (( )?) -- 4.11. The basic hook representations -- Bibliography -- Back Cover. 330 $a"We define and study cohomological tensor functors from the category Tn of finite-dimensional representations of the supergroup for the image of an arbitrary irreducible representation. In particular DS(L) is semisimple and multiplicity free. We derive a few applications of this theorem such as the degeneration of certain spectral sequences and a formula for the modified superdimension of an irreducible representation"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aTensor algebra 606 $aTensor products 606 $aNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Representations, algebraic theory (weights)$2msc 606 $aNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Simple, semisimple, reductive (super)algebras$2msc 606 $aNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Homological methods in Lie (super)algebras$2msc 606 $aCategory theory; homological algebra -- Categories with structure -- Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories$2msc 606 $aGroup theory and generalizations -- Linear algebraic groups and related topics -- Representation theory$2msc 615 0$aTensor algebra. 615 0$aTensor products. 615 7$aNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Representations, algebraic theory (weights). 615 7$aNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Simple, semisimple, reductive (super)algebras. 615 7$aNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Homological methods in Lie (super)algebras. 615 7$aCategory theory; homological algebra -- Categories with structure -- Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories. 615 7$aGroup theory and generalizations -- Linear algebraic groups and related topics -- Representation theory. 676 $a512/.57 686 $a17B10$a17B20$a17B55$a18D10$a20G05$2msc 700 $aHeidersdorf$b Thorsten$01801026 701 $aWeissauer$b Rainer$056493 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910957044903321 996 $aCohomological Tensor Functors on Representations of the General Linear Supergroup$94346065 997 $aUNINA