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
收藏
页码：995 / 1024
页数：30
相关论文
共 50 条
  • [1] Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type I. Non-semisimple classes in PSLn(q)
    Andruskiewitsch, Nicolas
    Carnovale, Giovanna
    Andres Garcia, Gaston
    JOURNAL OF ALGEBRA, 2015, 442 : 36 - 65
  • [2] Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VII. Semisimple classes in PSLn(q) and PSp2n(q)
    Andruskiewitsch, Nicolas
    Carnovale, Giovanna
    Garcia, Gaston Andres
    JOURNAL OF ALGEBRA, 2024, 639 : 354 - 397
  • [3] Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type II: Unipotent classes in symplectic groups
    Andruskiewitsch, Nicolas
    Carnovale, Giovanna
    Andres Garcia, Gaston
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2016, 18 (04)
  • [4] Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V. Mixed classes in Chevalley and Steinberg groups
    Nicolás Andruskiewitsch
    Giovanna Carnovale
    Gastón Andrés García
    manuscripta mathematica, 2021, 166 : 605 - 647
  • [5] Finite-Dimensional Pointed Hopf Algebras Over Finite Simple Groups of Lie Type IV. Unipotent Classes in Chevalley and Steinberg Groups
    Nicolás Andruskiewitsch
    Giovanna Carnovale
    Gastón Andrés García
    Algebras and Representation Theory, 2020, 23 : 621 - 655
  • [6] Finite-Dimensional Pointed Hopf Algebras Over Finite Simple Groups of Lie Type IV. Unipotent Classes in Chevalley and Steinberg Groups
    Andruskiewitsch, Nicolas
    Carnovale, Giovanna
    Andres Garcia, Gaston
    ALGEBRAS AND REPRESENTATION THEORY, 2020, 23 (03) : 621 - 655
  • [7] Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VI. Suzuki and Ree groups
    Carnovale, Giovanna
    Costantini, Mauro
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2021, 225 (04)
  • [8] Erratum to: Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V. Mixed classes in Chevalley and Steinberg groups
    Nicolás Andruskiewitsch
    Giovanna Carnovale
    Gastón Andrés García
    manuscripta mathematica, 2021, 166 : 649 - 649
  • [9] Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups
    Andruskiewitsch, Nicolas
    Carnovale, Giovanna
    Garcia, Gaston Andres
    MANUSCRIPTA MATHEMATICA, 2021, 166 (3-4) : 605 - 647
  • [10] Finite-dimensional simple-pointed Hopf algebras
    Radford, DE
    JOURNAL OF ALGEBRA, 1999, 211 (02) : 686 - 710
12345