A REPRESENTATION THEOREM FOR LYAPUNOV-LIKE TRANSFORMATIONS ON EUCLIDEAN JORDAN ALGEBRAS

A Lyapunov-like (linear) transformation L on a Euclidean Jordan algebra V is defined by the condition $$x \in K,\enspace y\in K^*,\quad \langle x,y\rangle =0\Rightarrow \langle L(x),y\rangle=0,$$where K is the symmetric cone of V. In this paper, we give an elementary proof (avoiding Lie algebraic ideas and results) of the fact that Lyapunov-like transformations on V are of the form La + D, where a ∈ V, D is a derivation, and La(x) = a ◦ x for all x ∈ V.

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Year of publication:	2013
Authors:	TAO, JIYUAN ; GOWDA, M. SEETHARAMA
Published in:	International Game Theory Review (IGTR). - World Scientific Publishing Co. Pte. Ltd., ISSN 1793-6675. - Vol. 15.2013, 04, p. 1340034-1
Publisher:	World Scientific Publishing Co. Pte. Ltd.
Subject:	Euclidean Jordan algebra \| symmetric cone \| Z and Lyapunov-like transformations

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Extent:	application/pdf text/html
Type of publication:	Article
Classification:	B4 - Economic Methodology ; C0 - Mathematical and Quantitative Methods. General ; C6 - Mathematical Methods and Programming ; C7 - Game Theory and Bargaining Theory ; D5 - General Equilibrium and Disequilibrium ; D7 - Analysis of Collective Decision-Making ; M2 - Business Economics
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011011318