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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hopf algebras with triality


Authors: Georgia Benkart, Sara Madariaga and José M. Pérez-Izquierdo
Journal: Trans. Amer. Math. Soc. 365 (2013), 1001-1023
MSC (2010): Primary 16T05, 20N05, 17D99
Published electronically: August 21, 2012
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Abstract: In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows us to give a new construction of the universal enveloping algebras of Malcev algebras. Our work relies on the approach of Grishkov and Zavarnitsine to groups with triality.


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Additional Information

Georgia Benkart
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: benkart@math.wisc.edu

Sara Madariaga
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006, Logroño, España
Email: sara.madariaga@unirioja.es

José M. Pérez-Izquierdo
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006, Logroño, España
Email: jm.perez@unirioja.es

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05656-X
PII: S 0002-9947(2012)05656-X
Keywords: Triality, Hopf algebras, Moufang-Hopf algebras, Moufang loops, Malcev algebras, Lie algebras, groups, nonassociative algebra
Received by editor(s): August 4, 2010
Received by editor(s) in revised form: November 7, 2010, and June 21, 2011
Published electronically: August 21, 2012
Additional Notes: The second and third authors would like to thank Spanish Ministerio de Educación y Ciencia and FEDER MTM 2007-67884-C04-03 and the University of La Rioja. The second author was also supported by the Spanish MICINN grant AP2007-01986 and ATUR 09/22.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.