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Associative and Lie algebras of quotients

Francesc Perera and Mercedes Siles Molina

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Abstract

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

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

Dates
First available in Project Euclid: 17 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.pm/1197908699

Mathematical Reviews number (MathSciNet)
MR2384843

Zentralblatt MATH identifier
1151.17010

Subjects
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}

Keywords
Lie algebra algebra of quotients multiplicative semiprime algebra dense extension

Citation

Perera, Francesc; Siles Molina, Mercedes. Associative and Lie algebras of quotients. Publ. Mat. 52 (2008), no. 1, 129--149. https://projecteuclid.org/euclid.pm/1197908699


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