Open Access
2008 Associative and Lie algebras of quotients
Francesc Perera, Mercedes Siles Molina
Publ. Mat. 52(1): 129-149 (2008).


In this paper we examine how the notion of algebra of quotients for Lie algebras ties up with the corresponding well-known concept in the associative case. Specifically, we completely characterize when a Lie algebra $Q$ is an algebra of quotients of a Lie algebra $L$ in terms of the associative algebras generated by the adjoint operators of $L$ and $Q$ respectively. In a converse direction, we also provide with new examples of algebras of quotients of Lie algebras and these come from associative algebras of quotients. In the course of our analysis, we make use of the notions of density and multiplicative semiprimeness to link our results with the maximal symmetric ring of quotients.


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Francesc Perera. Mercedes Siles Molina. "Associative and Lie algebras of quotients." Publ. Mat. 52 (1) 129 - 149, 2008.


Published: 2008
First available in Project Euclid: 17 December 2007

zbMATH: 1151.17010
MathSciNet: MR2384843

Primary: 16N60 , 16S90 , 17B60

Keywords: algebra of quotients , dense extension , Lie algebra , multiplicative semiprime algebra

Rights: Copyright © 2008 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.52 • No. 1 • 2008
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