Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type III. Semisimple classes in PSLn(q)

被引：9

作者：

Andruskiewitsch, Nicolas ^{[1
]}

Carnovale, Giovanna ^{[2
]}

Andres Garcia, Gaston ^{[3
]}

机构：

[1] Univ Nacl Cordoba, CIEM CONICET, FAMAF, Medina Allende S-N,Ciudad Univ, RA-5000 Cordoba, Argentina

[2] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Via Trieste 63, I-35121 Padua, Italy

[3] Univ Nacl La Plata, CONICET, Fac Ciencias Exactas, Dept Matemat, CC 172, RA-1900 La Plata, Buenos Aires, Argentina

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2017年 / 33卷 / 03期

关键词：

Nichols algebra; Hopf algebra; rack; finite group of Lie type; conjugacy class; NICHOLS ALGEBRAS; PROBABILISTIC GENERATION; CONJUGACY CLASSES; CLASSIFICATION; RACKS;

D O I：

10.4171/RMI/961

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective special linear group over a finite field, corresponding to semisimple orbits, have infinite dimension. We introduce a new criterium to determine when a conjugacy class collapses and prove that for infinitely many pairs (n, q), any finite-dimensional pointed Hopf algebra H with G(H) similar or equal to PSLn(q) or SLn(q) is isomorphic to a group algebra.

引用

页码：995 / 1024

页数：30

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