Superized Troesch complexes and cohomology for strict polynomial superfunctors |
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| Institution: | 1. Department of Mathematical Sciences, DePaul University, Chicago, IL 60614, USA;2. Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA;1. Utrecht University, Netherlands;2. University of Coimbra, CMUC, Department of Mathematics, Portugal;3. Polytechnic Institute of Viseu, ESTGV, Portugal;1. Sapientia Hungarian University of Transylvania, Târgu-Mure?/Corunca, Sighi?oarei road, nr. 2, Postal code: 540485, Romania;2. University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706, United States of America |
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| Abstract: | We adapt a construction due to Troesch to the category of strict polynomial superfunctors in order to construct complexes of injective objects whose cohomology is isomorphic to Frobenius twists of the (super)symmetric power functors. We apply these complexes to construct injective resolutions of the even and odd Frobenius twist functors, to investigate the structure of the Yoneda algebra of the Frobenius twist functor, and to compute other extension groups between strict polynomial superfunctors. By an equivalence of categories, this also provides cohomology calculations in the category of left modules over Schur superalgebras. |
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| Keywords: | Strict polynomial superfunctors Troesch complexes Hypercohomology spectral sequences |
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