Nonassociativity and Integrable Hierarchies
| dc.creator | Dimakis, Aristophanes | |
| dc.creator | Muller-Hoissen, Folkert | |
| dc.date | 2005-12-31 | |
| dc.date | 2006-06-13 | |
| dc.date.accessioned | 2026-07-07T06:59:33Z | |
| dc.date.available | 2026-07-07T06:59:33Z | |
| dc.description | Let A be a nonassociative algebra such that the associator (A,A^2,A) vanishes. If A is freely generated by an element f, there are commuting derivations delta_n, n=1,2,..., such that delta_n(f) is a nonlinear homogeneous polynomial in f of degree n+1. We prove that the expressions delta_{n_1} ... delta_{n_k}(f) satisfy identities which are in correspondence with the equations of the Kadomtsev-Petviashvili (KP) hierarchy. As a consequence, solutions of the `nonassociative hierarchy' partial_{t_n}(f) = delta_n(f), n=1,2,..., of ordinary differential equations lead to solutions of the KP hierarchy. The framework is extended by introducing the notion of an A-module and constructing, with the help of the derivations delta_n, zero curvature connections and linear systems. | |
| dc.description | 36 pages, second version substantially revised and rewritten | |
| dc.identifier | https://arxiv.org/abs/nlin/0601001 | |
| dc.identifier | http://arxiv.org/abs/nlin/0601001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107787 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | Nonassociativity and Integrable Hierarchies | |
| dc.type | text |