On the restricted Jordan plane in odd characteristic

被引：4
|
作者：
Andruskiewitsch, Nicolas [1 ]
Pena Pollastri, Hector [1 ]
机构：
[1] Univ Nacl Cordoba, CONICET, CIEM, Fac Matemat Astron & Fis, Medina Allende S-N,Ciudad Univ, RA-5000 Cordoba, Argentina
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2021年 / 20卷 / 01期
关键词：
Hopf algebras; Nichols algebras; Jordan plane; Drinfeld double; HOPF-ALGEBRAS;
D O I：
10.1142/S0219498821400120
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In positive characteristic the Jordan plane covers a finite-dimensional Nichols algebra that was described by Cibils et al. and we call the restricted Jordan plane. In this paper, the characteristic is odd. The defining relations of the Drinfeld double of the restricted Jordan plane are presented and its simple modules are determined. A Hopf algebra that deserves the name of double of the Jordan plane is introduced and various quantum Frobenius maps are described. The finite-dimensional pre-Nichols algebras intermediate between the Jordan plane and its restricted version are classified. The defining relations of the graded dual of the Jordan plane are given.
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页数：26
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