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On the restricted Jordan plane in odd characteristic
Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2020-07-22 , DOI: 10.1142/s0219498821400120
Nicolás Andruskiewitsch 1 , Héctor Peña Pollastri 1
Affiliation  

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.

中文翻译:

在奇特性的受限约旦平面上

在正特征中,Jordan 平面覆盖了 Cibils 等人描述的有限维 Nichols 代数。我们称之为受限约旦飞机。在本文中,特征是奇怪的。给出了受限Jordan平面的Drinfeld double的定义关系,并确定了它的简单模。介绍了一个名副其实的若尔当平面的Hopf代数,描述了各种量子Frobenius映射。在 Jordan 平面与其受限版本之间的有限维前 Nichols 代数被分类。给出了Jordan平面渐变对偶的定义关系。
更新日期:2020-07-22
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