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Abstract:

We give a complete classification of the 32-dimensional pointed Hopf algebras over an algebraically closed field k with char k ≠ 2. It turns out that there are infinite families of isomorphism classes of pointed Hopf algebras of dimension 32. In [AS1], [BDG] and [Ge] are given families of counterexamples for the tenth Kaplansky conjecture. Up to now, 32 is the lowest dimension where Kaplansky conjecture fails.

Registro:

Documento: Artículo
Título:Pointed Hopf algebras of dimension 32
Autor:Graña, M.
Filiación:Depto. de Matemática, Pab. I, Ciudad Universitaria, (1428) Buenos Aires, Argentina
Año:2000
Volumen:28
Número:6
Página de inicio:2935
Página de fin:2976
DOI: http://dx.doi.org/10.1080/00927870008827002
Título revista:Communications in Algebra
Título revista abreviado:Commun. Algebra
ISSN:00927872
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00927872_v28_n6_p2935_Grana

Referencias:

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  • Andruskiewitsch, N., Schneider, H.-J., Lifting of quantum linear spaces and pointed Hopf algebras of order p3 (1998) J.Algebra, 209, pp. 659-691
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  • Andruskiewitsch, N., Schneider, H.-J., Pointed Hopf Algebras of Dimension p4, , in preparation
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  • Dǎscǎlescu, S., Pointed Hopf Algebras of Dimension pn with Large Coradical, , preprint
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  • Gelaki, S., On pointed Hopf algebras and Kaplansky's tenth conjecture (1998) J.Algebra, 209, pp. 635-657
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Citas:

---------- APA ----------
(2000) . Pointed Hopf algebras of dimension 32. Communications in Algebra, 28(6), 2935-2976.
http://dx.doi.org/10.1080/00927870008827002
---------- CHICAGO ----------
Graña, M. "Pointed Hopf algebras of dimension 32" . Communications in Algebra 28, no. 6 (2000) : 2935-2976.
http://dx.doi.org/10.1080/00927870008827002
---------- MLA ----------
Graña, M. "Pointed Hopf algebras of dimension 32" . Communications in Algebra, vol. 28, no. 6, 2000, pp. 2935-2976.
http://dx.doi.org/10.1080/00927870008827002
---------- VANCOUVER ----------
Graña, M. Pointed Hopf algebras of dimension 32. Commun. Algebra. 2000;28(6):2935-2976.
http://dx.doi.org/10.1080/00927870008827002