Eur. Phys. J. B 29, 177-181 (2002)
https://doi.org/10.1140/epjb/e2002-00281-y

Complexifications and real forms of structures

¹ Institute for Nuclear Research and Nuclear Energy, 72 Tzarigradsko chaussée, 1784 Sofia, Bulgaria
² Dipartimento di Fisica “E.R.Caianiello”, Universita di Salerno and Istituto Nazionale di fisica Nucleare, Gruppo Collegato di Salerno, via S. Aliende, Salerno, Italy
³ Dipartimento di Scienze Fisiche, Università Federico II di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte Sant'Angelo, Via Cintia, 80126 Napoli, Italy

Corresponding author: ^a gerjikov@inrne.bas.bg

Received: 18 October 2001
Revised: 24 May 2002
Published online: 2 October 2002

Abstract

We consider generalizations of the standard dynamics to complex dynamical variables and introduce the notions of real form in analogy with the notion of real forms for a simple Lie algebra. Thus to each real system we are able to relate several nonequivalent ones. On the example of the complex Toda chain we demonstrate how starting from a known integrable system (e.g. the Toda chain) one can complexify it and then project onto different real forms.