Co-Frobenius Hopf algebras and the coradical filtration

被引：0
|
作者：
N. Andruskiewitsch
S. Dascalescu
机构：
[1] Facultad de Matemática,
[2] Astronomía y Física,undefined
[3] CIEM-CONICET,undefined
[4] Universidad Nacional de Córdoba,undefined
[5] (5000) Ciudad Universitaria,undefined
[6] Córdoba. Argentina (e-mail: andrus@mate.uncor.edu) ,undefined
[7] Facultatea de Matematica,undefined
[8] University of Bucharest,undefined
[9] Str. Academiei 14,undefined
[10] 70109 Bucharest 1,undefined
[11] Romania ,undefined
[12] Faculty of Science,undefined
[13] Kuwait University,undefined
[14] Department of Mathematics & Computer Science,undefined
[15] PO Box 5969,undefined
[16] Safat 13060,undefined
[17] Kuwait (e-mail: sdascal@al.math.unibuc.ro,undefined
[18] sdascal@mcs.sci.kuniv.edu.kw),undefined
来源：
Mathematische Zeitschrift | 2003年 / 243卷
关键词：
Mathematics Subject Classification (2000): 16W30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove that a Hopf algebra with a finite coradical filtration is co-Frobenius. We also characterize co-Frobenius Hopf algebras with coradical a Hopf subalgebra. Let H be a Hopf algebra whose coradical is a Hopf algebra. Let gr H be the associated graded coalgebra and let R be the diagram of H, c. f. [2]. Then the following are equivalent: (1) H is co-Frobenius; (2) gr H is co-Frobenius; (3) R is finite dimensional; (4) the coradical filtration of H is finite. This Theorem allows us to give systematically examples of co-Frobenius Hopf algebras, and opens the way to the classification of ample classes of such Hopf algebras.
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页码：145 / 154
页数：9
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