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Associative and Lie algebras of quotients

Francesc Perera and Mercedes Siles Molina

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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.

Article information

Publ. Mat., Volume 52, Number 1 (2008), 129-149.

First available in Project Euclid: 17 December 2007

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Zentralblatt MATH identifier

Primary: 17B60: Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 16N60: Prime and semiprime rings [See also 16D60, 16U10] 16S90: Torsion theories; radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx}

Lie algebra algebra of quotients multiplicative semiprime algebra dense extension


Perera, Francesc; Siles Molina, Mercedes. Associative and Lie algebras of quotients. Publ. Mat. 52 (2008), no. 1, 129--149.

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