The Differential Graded Odd NilHecke Algebra

Ellis, Alexander P.; Qi, You

doi:10.1007/s00220-015-2569-4

Cited by 10 publications

(6 citation statements)

References 57 publications

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“…The representation-theoretic interpretation of odd Khovanov homology is substantially more involved than that of Khovanov homology, and is still an active area of research (see, for instance, [143,127,43,100]).…”

Section: Signs and Spectral Sequencesmentioning

confidence: 99%

Categorical lifting of the Jones polynomial: a survey

Khovanov¹,

Lipshitz²

2022

Preprint

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Section: Signs and Spectral Sequencesmentioning

confidence: 99%

Categorical lifting of the Jones polynomial: a survey

Khovanov¹,

Lipshitz²

2022

Preprint

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“…The nilHecke category should then be replaced by the odd nilHecke algebra of [EKL14]. We refer the reader to [EQ15b] for the details. But a natural question still remains: Can one lift the constructions in positive characteristics to characteristic zero?…”

Section: -Morphism Generatormentioning

confidence: 99%

Categorification at prime roots of unity and hopfological finiteness

Qi¹,

Sussan²

2017

Categorification and Higher Representation Theory

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We survey some recent results in hopfological algebra and the program of categorification at prime roots of unity. A categorical Jones-Wenzl projector at prime roots of unity is studied, and it is shown that this projector is hopfologically finite in special characteristics, while generically it is infinite.2010 Mathematics Subject Classification. Primary 81R50; Secondary 16E20, 16E35. Key words and phrases. Categorification, hopfological algebra, prime roots of unity. The authors are very grateful to Mikhail Khovanov for his support and encouragement, as well as sharing with us his insights on the subject. The authors would also like to thank Catharina Stroppel for helpful discussions about categorifying Jones-Wenzl projectors.

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“…We expect that a similar construction can be extended to the sl 3 case by combining Stošić's sl 3 -thick calculus ( [Sto15] ) with the differential defined in [KQ15], which will then categorify the quantum Frobenius map for the upper half of sl 3 at a prime root of unity. Likewise, a careful modification of the previous construction in the DG odd nilHecke algebra case [EQ16c] will give rise to a characteristic-zero lifting of the quantum Frobenius map for sl 2 at a fourth root of unity. Remark 3.20.…”

Section: Unoriented Graphical Calculusmentioning

confidence: 99%