Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups

被引:5
作者
Andruskiewitsch, Nicolas [1 ]
Carnovale, Giovanna [2 ]
Garcia, Gaston Andres [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, Fac Ciencias Exactas, Dept Matemat, CONICET, CC 172, RA-1900 La Plata, Argentina
关键词
CONJUGACY CLASSES;
D O I
10.1007/s00229-020-01248-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from PSLn(q) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is PSp(2n)(q), P Omega(+)(4n)(q), P Omega(-)(4n)(q), D-3(4)(q), E-7(q), E-8(q), F-4(q), or G(2)(q) with q even is the group algebra.
引用
收藏
页码:605 / 647
页数:43
相关论文
共 27 条
[21]  
Malle G., 2011, CAMBR STUD ADV MATH, V133
[22]   Component groups of unipotent centralizers in good characteristic [J].
McNinch, GJ ;
Sommers, E .
JOURNAL OF ALGEBRA, 2003, 260 (01) :323-337
[23]  
Schonert Martin, 1997, GAP GROUPS ALGORITHM
[24]  
Springer T. A., 1970, Seminar on algebraic groups and related finite groups (The Institute for Advanced Study, Princeton, NJ, 1968/69), P167, DOI DOI 10.1007/BFB0081546
[25]  
Springer T.A., 1998, Linear Algebraic Groups, VSecond
[26]  
STEINBER.R, 1968, MEM AM MATH SOC, P1
[27]  
STEINBERG R., 1968, Lectures on Chevalley Groups