Kurush Ebrahimi-Fard, Alexander Lundervold, Igor Mencattini, Hans Z. Munthe-Kaas, “Post-Lie Algebras and Isospectral Flows”, SIGMA, 2015, Volume 11,093, 16 pp.

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SIGMA, 2015 Volume 11, 093, 16 pp. (Mi sigma1074)

This article is cited in 18 papers

Post-Lie Algebras and Isospectral Flows

Kurush Ebrahimi-Fard^a, Alexander Lundervold^b, Igor Mencattini^c, Hans Z. Munthe-Kaas^d

^a ICMAT, C/Nicolás Cabrera 13-15, 28049 Madrid, Spain
^b Department of Computing, Mathematics and Physics, Faculty of Engineering, Bergen University College, Postbox 7030, N-5020 Bergen, Norway
^c Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil
^d Department of Mathematics, University of Bergen, Postbox 7803, N-5020 Bergen, Norway

Abstract: In this paper we explore the Lie enveloping algebra of a post-Lie algebra derived from a classical $R$-matrix. An explicit exponential solution of the corresponding Lie bracket flow is presented. It is based on the solution of a post-Lie Magnus-type differential equation.

Keywords: isospectral flow equation; $R$-matrix; Magnus expansion; post-Lie algebra.

MSC: 70H06; 17D99; 37J35

Received: August 13, 2015; in final form November 16, 2015; Published online November 20, 2015

Language: English

DOI: 10.3842/SIGMA.2015.093

Bibliographic databases:

ArXiv: 1505.02436

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