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Akademický článek
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Autor:
Pavel Etingof, Shlomo Gelaki
Publikováno v:
arXiv
We prove that every finite symmetric integral tensor category $\mathcal{C}$ with the Chevalley property over an algebraically closed field $k$ of characteristic $p>2$ admits a symmetric fiber functor to the category of supervector spaces. This proves
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c1c02ba0981381446b98c7c125a684e9
https://hdl.handle.net/1721.1/134023
https://hdl.handle.net/1721.1/134023
Publikováno v:
Annals of Mathematics. 197
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f14f9aee5cee50b4977761c31b80d410
https://doi.org/10.4007/annals.2023.197.3.5
https://doi.org/10.4007/annals.2023.197.3.5
Autor:
Kevin Coulembier, Ivan Penkov
Publikováno v:
Moscow Mathematical Journal. 19:655-693
We study a version of the BGG category O for Dynkin Borel subalgebras of root-reductive Lie algebras g, such as gl(\infty). We prove results about extension fullness and compute the higher extensions of simple modules by Verma modules. In addition, w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::744677604978f4526d420b141ee87081
https://doi.org/10.17323/1609-4514-2019-19-4-655-693
https://doi.org/10.17323/1609-4514-2019-19-4-655-693
Autor:
Kevin Coulembier
Publikováno v:
Mathematische Zeitschrift. 295:821-837
We classify all equivalences between the indecomposable abelian categories which appear as blocks in BGG category $${\mathcal {O}}$$ for reductive Lie algebras. Our classification implies that a block in category $${\mathcal {O}}$$ only depends on th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dd851c495448b1b8bfdeb30967dff226
https://doi.org/10.1007/s00209-019-02376-9
https://doi.org/10.1007/s00209-019-02376-9
Publikováno v:
Mathematical Research Letters. 26:447-499
We study the problem of indecomposability of translations of simple modules in the principal block of BGG category O for sl(n), as conjectured in [KiM1]. We describe some general techniques and pro ...
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https://explore.openaire.eu/search/publication?articleId=doi_________::47ca5ea7fb6dfb42fcdc59c78dd3170f
https://doi.org/10.4310/mrl.2019.v26.n2.a5
https://doi.org/10.4310/mrl.2019.v26.n2.a5
We study abelian envelopes for pseudo-tensor categories with the property that every object in the envelope is a quotient of an object in the pseudo-tensor category. We establish an intrinsic criterion on pseudo-tensor categories for the existence of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8c1165b6db66a14ab6d32c8855b58d2d
Autor:
Kevin Coulembier
We study how tensor categories can be presented in terms of rigid monoidal categories and Grothendieck topologies and show that such presentations lead to strong universal properties. As the main tool in this study, we define a notion on preadditive
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8665c967e357809d62798b3677862f51
http://arxiv.org/abs/2011.02137
http://arxiv.org/abs/2011.02137
Autor:
Kevin Coulembier
We demonstrate equivalence between two definitions of lower finite highest weight categories. We also show that, in the presence of a duality, a lower finite highest weight structure on a category is unique. Finally, we give a proof for the known fac
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::da144ac2020f0a920401bead5d02001a