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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Linearly compact algebraic Lie algebras
and coalgebraic Lie coalgebras


Authors: Bienvenido Cuartero, José E. Galé and Arkadii M. Slinko
Journal: Proc. Amer. Math. Soc. 125 (1997), 1945-1952
MSC (1991): Primary 17B99
MathSciNet review: 1376754
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Abstract: It is proved that if the dual Lie algebra of a Lie coalgebra is algebraic, then it is algebraic of bounded degree. This result is an analog of the D.Radford's result for associative coalgebras.


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Additional Information

Bienvenido Cuartero
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: cuartero@cc.unizar.es

José E. Galé
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: gale@cc.unizar.es

Arkadii M. Slinko
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019 Auckland, New Zealand
Email: a.slinko@auckland.ac.nz

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03794-5
PII: S 0002-9939(97)03794-5
Keywords: Lie coalgebra, dual Lie algebra, algebraic Lie algebra of bounded degree
Received by editor(s): August 31, 1995
Received by editor(s) in revised form: January 25, 1996
Additional Notes: The research of the first two authors has been partially supported by the Project PS090-0120, DGICYT, Spain.
This paper was written when the third author visited Universities of Oviedo and Zaragoza in January–February $1995$. It is his great pleasure to express his gratitude to both Departments of Mathematics for the hospitality and DGICYT (PS 90–0120) and The University of Oviedo for the financial support.
Communicated by: Roe W. Goodman
Article copyright: © Copyright 1997 American Mathematical Society