2002/01/10 by Janusz Grabowski, Giuseppe Marmo
Mathematics · #math.DG #math.OA #msc:17B65 #msc:81R10 #msc:17B63 #msc:37J99 #msc:53D99 #msc:70H99
published as in: Classical and Quantum Integrability, J. Grabowski and P. Urbanski (eds.), Banach Center Publ. 59 (2003), 163-172 · 10 pages, conference Classical and Quantum Integrability, Warszawa, 27-30 August, 2001
arxiv created 2002/01/10 · arxiv updated 2009/11/30
Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply the properties which usually are additionally required. In particular, it is proved that locality of a Loday bracket on sections of a one-dimensional vector bundle forces skew-symmetry, i.e. a local Lie algebra structure in the sense of A.A.Kirillov.