scholarly journals Hopf algebras of prime dimension in positive characteristic

2019 ◽  
Vol 51 (3) ◽  
pp. 459-465
Author(s):  
Siu‐Hung Ng ◽  
Xingting Wang
Keyword(s):  
Hopf Algebras ◽  
Positive Characteristic ◽  
Prime Dimension

scholarly journals Indicators of Hopf algebras in positive characteristic

2018 ◽  
Vol 111 (5) ◽  
pp. 485-491
Author(s):  
Linhong Wang ◽  
Xingting Wang
Keyword(s):  
Hopf Algebras ◽  
Positive Characteristic

scholarly journals Pointed p3-Dimensional Hopf Algebras in Positive Characteristic

2018 ◽  
Vol 25 (03) ◽  
pp. 399-436
Author(s):  
Van C. Nguyen ◽  
Xingting Wang
Keyword(s):  
Group Algebra ◽  
Hopf Algebras ◽  
Positive Characteristic ◽  
Group Algebras ◽  
Closed Field ◽  
Graded Algebra ◽  
Prime Characteristic ◽  
Characteristic P ◽  
Finite Dimensional

We focus on the classification of pointed p3-dimensional Hopf algebras H over any algebraically closed field of prime characteristic p > 0. In particular, we consider certain cases when the group of grouplike elements is of order p or p2, that is, when H is pointed but is not connected nor a group algebra. The structures of the associated graded algebra gr H are completely described as bosonizations of graded braided Hopf algebras over group algebras, and most of the lifting structures of H are given. This work provides many new examples of (parametrized) non-commutative, non-cocommutative finite-dimensional Hopf algebras in positive characteristic.

Left counital Hopf algebras on bi-decorated planar rooted forests and Rota-Baxter systems

2020 ◽  
Vol 27 (2) ◽  
pp. 219-243 ◽  
Author(s):  
Xiao-Song Peng ◽  
Yi Zhang ◽  
Xing Gao ◽  
Yan-Feng Luo
Keyword(s):  
Hopf Algebras

scholarly journals Monadic cointegrals and applications to quasi-Hopf algebras

2021 ◽  
Vol 225 (10) ◽  
pp. 106678
Author(s):  
Johannes Berger ◽  
Azat M. Gainutdinov ◽  
Ingo Runkel
Keyword(s):  
Hopf Algebras
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