In this paper we apply our recent geometric theory of noncommuttive (quantum) manifolds and noncommutative (quantum) PDEs , to the category of quantum quaternionic manifolds. These are manifolds modelled on spaces built starting from quaternionic algebras. For PDEs considered in such category we determine theorems of existence of local and global quaternionic solutions. We show also that such a category of quantum quaternionic manifolds properly contains that of manifolds with (almost) quaternionic structure. So our theorems of existence of quantum quaternionic manifolds for PDEs produce a cascade of new solutions with nontrivial topology.

Theorems of existence of local and global solutions of PDE's in the category of noncommutative quaternionic manifolds / Prastaro, Agostino. - STAMPA. - (2001), pp. 329-337.

Theorems of existence of local and global solutions of PDE's in the category of noncommutative quaternionic manifolds

PRASTARO, Agostino
2001

Abstract

In this paper we apply our recent geometric theory of noncommuttive (quantum) manifolds and noncommutative (quantum) PDEs , to the category of quantum quaternionic manifolds. These are manifolds modelled on spaces built starting from quaternionic algebras. For PDEs considered in such category we determine theorems of existence of local and global quaternionic solutions. We show also that such a category of quantum quaternionic manifolds properly contains that of manifolds with (almost) quaternionic structure. So our theorems of existence of quantum quaternionic manifolds for PDEs produce a cascade of new solutions with nontrivial topology.
2001
Quaternionic Structures in Mathematics and Physics
02 Pubblicazione su volume::02a Capitolo o Articolo
Theorems of existence of local and global solutions of PDE's in the category of noncommutative quaternionic manifolds / Prastaro, Agostino. - STAMPA. - (2001), pp. 329-337.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/149051
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