04741nam 22006613 450 991095704490332120231110230541.097814704652851470465280(CKB)4100000011975358(MiAaPQ)EBC6661105(Au-PeEL)EBL6661105(OCoLC)1259594040(RPAM)22488172(EXLCZ)99410000001197535820210901d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierCohomological Tensor Functors on Representations of the General Linear Supergroup1st ed.Providence :American Mathematical Society,2021.©2021.1 online resource (118 pages)Memoirs of the American Mathematical Society ;v.2709781470447144 1470447142 Includes bibliographical references.Cover -- 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 &gt -- 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 (( )ⁿ) -- 4.11. The basic hook representations -- Bibliography -- Back Cover."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"--Provided by publisher.Memoirs of the American Mathematical Society Tensor algebraTensor productsNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Representations, algebraic theory (weights)mscNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Simple, semisimple, reductive (super)algebrasmscNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Homological methods in Lie (super)algebrasmscCategory theory; homological algebra -- Categories with structure -- Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categoriesmscGroup theory and generalizations -- Linear algebraic groups and related topics -- Representation theorymscTensor algebra.Tensor products.Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Representations, algebraic theory (weights).Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Simple, semisimple, reductive (super)algebras.Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Homological methods in Lie (super)algebras.Category theory; homological algebra -- Categories with structure -- Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories.Group theory and generalizations -- Linear algebraic groups and related topics -- Representation theory.512/.5717B1017B2017B5518D1020G05mscHeidersdorf Thorsten1801026Weissauer Rainer56493MiAaPQMiAaPQMiAaPQBOOK9910957044903321Cohomological Tensor Functors on Representations of the General Linear Supergroup4346065UNINA