A basis theorem for the affine Kauffman category and its cyclotomic quotients

Gao, Mengmeng; Rui, Hebing; Song, Linliang

doi:10.1016/j.jalgebra.2022.07.005

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Cited by 6 publications

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“…The generalisation of the first functor should follow from the results [LZZ20], and then the affine case follows from the general affinisation procedure of [MS21]. Once again, analogues exist in the orthosymplectic case, where the relevant categories are the Kauffman skein category , together with its affine analogue introduced in [GRS22].…”

Section: Introductionmentioning

confidence: 99%

The Quantum Isomeric Supercategory

Savage

2023

J. Inst. Math. Jussieu

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Section: Introductionmentioning

confidence: 99%

The Quantum Isomeric Supercategory

Savage

2023

J. Inst. Math. Jussieu

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“…Its endomorphism algebras are the BMW algebras introduced in [BW89] and [Mur87], and it has been used to study the representation theory of the quantum enveloping algebras of the special orthogonal and symplectic Lie algebras, U q (so m ) and U q (sp 2n ). Affine BMW algebras were defined in [OR07], and a corresponding affine version of the Kauffmann category first appeared in the literature in [GRS22]. This category was previously defined in terms of string diagrams on an annulus by Kevin Walker; his as-yet-unpublished joint work with Monica Vazirani on the category was discussed in [Vaz].…”

Section: Introductionmentioning

confidence: 99%

Affine oriented Frobenius Brauer categories

McSween

Savage

2022

Communications in Algebra

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We define the affine Frobenius Brauer category AB(A, − ⋆ ) associated to each symmetric involutive Frobenius superalgebra A. We then define an action of these categories on the categories of finite-dimensional supermodules for orthosymplectic Lie superalgebras defined over A. The case where A is the base field recovers the known action of the affine Brauer category on categories of supermodules for orthogonal and symplectic Lie algebras. The definition and associated action of AB(A, − ⋆ ) are both novel when A is e.g. the quaternions H, a finite group algebra, a zigzag superalgebra, or a truncated polynomial algebra. Finally, we state a conjecture for bases of hom-spaces in AB(A, − ⋆ ) and outline a potential proof strategy.

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