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Abstract:

A fundamental step in the classification of finite-dimensional complex pointed Hopf algebras is the determination of all finite-dimensional Nichols algebras of braided vector spaces arising from groups. The most important class of braided vector spaces arising from groups is the class of braided vector spaces (ℂX, cq), where X is a rack and q is a 2-cocycle on X with values in ℂx. Racks and cohomology of racks appeared also in the work of topologists. This leads us to the study of the structure of racks, their cohomology groups and the corresponding Nichols algebras. We will show advances in these three directions. We classify simple racks in group-theoretical terms; we describe projections of racks in terms of general cocycles; we introduce a general cohomology theory of racks containing properly the existing ones. We introduce a "Fourier transform" on racks of certain type; finally, we compute some new examples of finite-dimensional Nichols algebras. © 2003 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:From racks to pointed Hopf algebras
Autor:Andruskiewitsch, N.; Graña, M.
Filiación:Facultad de Mat. Astronomia/Fisica, Universidad Nacional de Cordoba, CIEM-CONICET, 5000 Córdoba, Argentina
MIT, Mathematics Department, 77 Mass. Ave., Cambridge, MA 02139, United States
FCEyN-UBA, 1428 Buenos Aires, Argentina
Palabras clave:Pointed Hopf algebras; Quandles; Racks
Año:2003
Volumen:178
Número:2
Página de inicio:177
Página de fin:243
DOI: http://dx.doi.org/10.1016/S0001-8708(02)00071-3
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.
ISSN:00018708
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00018708_v178_n2_p177_Andruskiewitsch.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v178_n2_p177_Andruskiewitsch

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Citas:

---------- APA ----------
Andruskiewitsch, N. & Graña, M. (2003) . From racks to pointed Hopf algebras. Advances in Mathematics, 178(2), 177-243.
http://dx.doi.org/10.1016/S0001-8708(02)00071-3
---------- CHICAGO ----------
Andruskiewitsch, N., Graña, M. "From racks to pointed Hopf algebras" . Advances in Mathematics 178, no. 2 (2003) : 177-243.
http://dx.doi.org/10.1016/S0001-8708(02)00071-3
---------- MLA ----------
Andruskiewitsch, N., Graña, M. "From racks to pointed Hopf algebras" . Advances in Mathematics, vol. 178, no. 2, 2003, pp. 177-243.
http://dx.doi.org/10.1016/S0001-8708(02)00071-3
---------- VANCOUVER ----------
Andruskiewitsch, N., Graña, M. From racks to pointed Hopf algebras. Adv. Math. 2003;178(2):177-243.
http://dx.doi.org/10.1016/S0001-8708(02)00071-3