Rank three Nichols algebras of diagonal type over arbitrary fields

Wang, Jing

doi:10.1007/s11856-017-1456-4

Cited by 12 publications

(20 citation statements)

References 36 publications

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“…In this section, we recall the notations of semi-Cartan graphs, root systems, and Weyl groupoids. We mainly follow the terminology from [20,39] (see also [35][36][37]). Definition 6.…”

Section: Weyl Groupoidsmentioning

confidence: 99%

“…Towards this direction, new examples of Nichols algebras in positive characteristic and a combinatorial formula to study the relations in Nichols algebras were found [34]. Over fields of positive characteristic, rank 2, rank 3, and rank 4 finite dimensional Nichols algebras of diagonal type were listed in [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

“…Besides, the notations and conventions in [35][36][37] are followed, and several results from these papers will be used.…”

Section: Introductionmentioning

confidence: 99%

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Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type

Chen

Wang

2021

Advances in Mathematical Physics

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Nichols algebras are fundamental objects in the construction of quantized enveloping algebras and in the classification of pointed Hopf algebras by the lifting method of Andruskiewitsch and Schneider. The structure of Cartan graphs can be attached to any Nichols algebras of diagonal type and plays an important role in the classification of Nichols algebras of diagonal type with a finite root system. In this paper, the main properties of all simply connected Cartan graphs attached to rank 6 Nichols algebras of diagonal type are determined. As an application, we obtain a subclass of rank 6 finite dimensional Nichols algebras of diagonal type.

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“…In this section, we recall the notations of semi-Cartan graphs, root systems, and Weyl groupoids. We mainly follow the terminology from [20,39] (see also [35][36][37]). Definition 6.…”

Section: Weyl Groupoidsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type

Chen

Wang

2021

Advances in Mathematical Physics

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“…If λ 2 = 0 = µ 1 , then µ 3 = 0 and we can take µ 4 ∈ I 0,1 by rescaling x, which gives two classes of H described in (32) and (33).…”

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confidence: 99%

On non-connected pointed Hopf algebras of dimension 16 in characteristic 2

Xiong

2019

Preprint

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Let k be an algebraically closed field. We give a complete isomorphism classification of non-connected pointed Hopf algebras of dimension 16 with char k = 2 that are generated by group-like elements and skew-primitive elements. It turns out that there are infinitely many classes (up to isomorphism) of pointed Hopf algebras of dimension 16. In particular, we obtain infinitely many new examples of non-commutative non-cocommutative finite-dimensional pointed Hopf algebras.

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“…Towards this direction, new examples of Nichols algebras in positive characteristic and a combinatorial formula to study the relations in Nichols algebras were found [11]. Over fields of positive characteristic, rank 2 and rank 3 finite dimensional Nichols algebras of diagonal type were listed in [25,38]. In…”

mentioning

confidence: 99%