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NON-ABELIAN HOMOLOGY OF LIE ALGEBRAS

Published online by Cambridge University Press:  19 May 2004

N. INASSARIDZE ,
E. KHMALADZE  and
M. LADRA
N. INASSARIDZE
Affiliation:
A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Alexidze St. 1, Tbilisi 0193, Georgia e-mail: [email protected]@rmi.acnet.ge
E. KHMALADZE
Affiliation:
A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Alexidze St. 1, Tbilisi 0193, Georgia e-mail: [email protected]@rmi.acnet.ge
M. LADRA
Affiliation:
Departamento de Algebra, Facultad de Matemáticas, Universidad de Santiago de Compostela, Santiago de Compostela 15782, Spain e-mail: [email protected]
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Abstract

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Non-abelian homology of Lie algebras with coefficients in Lie algebras is constructed and studied, generalising the classical Chevalley-Eilenberg homology of Lie algebras. The relationship between cyclic homology and Milnor cyclic homology of non-commutative associative algebras is established in terms of the long exact non-abelian homology sequence of Lie algebras. Some explicit formulae for the second and the third non-abelian homology of Lie algebras are obtained.

Keywords

17B4017B5618G1018G50
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 2 , May 2004 , pp. 417 - 429
Copyright
2004 Glasgow Mathematical Journal Trust