Two-dimensional topological theories, rational functions and their tensor envelopes

Khovanov, Mikhail; Ostrik, Victor; Yakov, Kononov,

doi:10.1007/s00029-022-00785-z

Cited by 5 publications

(3 citation statements)

References 27 publications

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“…In this section, we specify our results to the case of DCob c for c ∈ k \ {0} and identify the images of indecomposable objects under the semisimplification functor. To this end, we recall that the semisimplification is given by Rep + osp(1|2) by a theorem of [KOK22]. We further clarify the relationship of DCob c to Deligne's category Rep(O −1 ) and its semisimplification.…”

Section: Special Cases and Examplesmentioning

confidence: 90%

“…In this section, α ∈ k[[t]] for k a splitting field for u α . We will relate the classification of indecomposable objects in DCob α to the tensor decomposition of these categories obtained in [KOK22]. If u α has a unique root, we prove the following.…”

Section: We Denote the Set Of Isomorphism Classes Of Irreducible Obje...mentioning

confidence: 95%

“…Subsequently, Khovanov-Kononov-Ostrik [KOK22] further investigated the categories DCob α . They proved that DCob α decomposes as an external tensor product of such tensor categories based on a partial fraction decomposition of α and identified semisimple quotients of these categories.…”

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confidence: 99%

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Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories

Flake

Laugwitz

Posur

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Section: Special Cases and Examplesmentioning

confidence: 90%

Section: We Denote the Set Of Isomorphism Classes Of Irreducible Obje...mentioning

confidence: 95%

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Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories

Flake

Laugwitz

Posur

2023

Advances in Mathematics

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Deligne Categories and Representations of the Finite General Linear Group, Part 1: Universal Property

Entova-Aizenbud,

Heidersdorf

2024

Transformation Groups

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We study the Deligne interpolation categories $$\underline{\textrm{Rep}}(GL_{t}({\mathbb F}_q))$$ Rep ̲ ( G L t ( F q ) ) for $$t\in \mathbb {C}$$ t ∈ C , first introduced by F. Knop. These categories interpolate the categories of finite-dimensional complex representations of the finite general linear group $$GL_n(\mathbb {F}_q)$$ G L n ( F q ) . We describe the morphism spaces in this category via generators and relations. We show that the generating object of this category (an analogue of the representation $${\mathbb C}{\mathbb F}_q^n$$ C F q n of $$GL_n(\mathbb {F}_q)$$ G L n ( F q ) ) carries the structure of a Frobenius algebra with a compatible $${\mathbb F}_q$$ F q -linear structure; we call such objects $$\mathbb {F}_q$$ F q -linear Frobenius spaces and show that $$\underline{\textrm{Rep}}(GL_{t}({\mathbb F}_q))$$ Rep ̲ ( G L t ( F q ) ) is the universal symmetric monoidal category generated by such an $$\mathbb {F}_q$$ F q -linear Frobenius space of categorical dimension t. In the second part of the paper, we prove a similar universal property for a category of representations of $$GL_{\infty }(\mathbb {F}_q)$$ G L ∞ ( F q ) .

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Invariants of r-spin TQFTs and non-semisimplicity

Carqueville,

Meir,

Szegedy

2025

Journal of Algebra

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Two-dimensional topological theories, rational functions and their tensor envelopes

Cited by 5 publications

References 27 publications

Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories

Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories

Deligne Categories and Representations of the Finite General Linear Group, Part 1: Universal Property

Invariants of r-spin TQFTs and non-semisimplicity

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