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Linearly compact algebraic Lie algebras and coalgebraic Lie coalgebras
Author(s):
Bienvenido
Cuartero;
José
E.
Galé;
Arkadii
M.
Slinko
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1945-1952.
MSC (1991):
Primary 17B99
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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.
References:
- 1.
- Y. Bakhturin, A. Mikhalev, V. Petrogradsky and M. Zaicev, Infinite dimensional Lie Superalgebras. Walter de Gruyter and Co, Berlin-New York, 1992.
- 2.
- N. Bourbaki, Espaces Vectoriels Topologiques (Chap. 1 et 2). Hermann, Paris, 1966. MR 34:3277
- 3.
- B. Cuartero and J.E. Galé, Locally PI-algebras over valued fields, In: Aportaciones Matematicas en Memoria del Profesor V.M.Onieva , Santander, Universidad de Cantabria, 1991, pp. 137-145. MR 92h:46112
- 4.
- B. Cuartero and J.E. Galé, Bounded Degree of Algebraic Topological Algebras, Communications in Algebra, 22(1) (1994), 329-337. MR 94m:17002
- 5.
- B. Cuartero, J.E. Galé, A. Rodriguez Palacios and A. Slinko, Bounded Degree of Weakly Algebraic Topological Lie Algebras, Manuscripta Math. 81 (1993), 129-139. MR 94k:17008
- 6.
- I. Kaplansky, Topological Methods in Valuation Theory, Duke Math. J. 14 (1947), 527-541. MR 9:172f
- 7.
- I. Kaplansky, Infinite abelian groups. University of Michigan Press, 1954. MR 16:444g
- 8.
- D.E. Radford, Coalgebraic Coalgebras, Proc. Amer. Math. Soc. 45 (1974), 11-18. MR 50:9942
- 9.
- A. Slinko, Local Finiteness of Coalgebraic Lie Coalgebras, Communications in Algebra, 23(3) (1995), 1165-1170. CMP 95:08
- 10.
- A. Slinko, Linearly Compact Algebras and Coalgebras, New Zealand Math. J., to appear. CMP 96:15
- 11.
- S. Warner, Linearly Compact Rings and Modules, Math Ann. 197 (1972), 29-43. MR 45:6874
- 12.
- E.I. Zelmanov, Nil Rings and Periodic Groups. KMS Lecture Notes in Mathematics, Korean Math. Soc., Seoul, 1992. MR 94c:16027
- 13.
- E.I. Zelmanov, On Periodic Compact Groups, Israel J. Math., 77 (1992), 83-95. MR 94e:20055
- 14.
- E.I. Zelmanov, On the Restricted Burnside Problem. In: Proceedings of the International Congress of Mathematicians, Kyoto, Japan, 1990, The Mathematical Society of Japan, 1991, pp. 395-402. MR 93d:20076
- 15.
- K.A. Zhevlakov, A.M. Slinko, I.P. Shestakov, A.I. Shirshov, Rings that are nearly associative, Academic Press, New York - London, 1982, pp. 371. MR 83i:17001
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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:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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