Division Algebras and Extended SuperKdVs
F. Toppan (CBPF)
TL;DR
This paper explores how division algebras can be used to construct supersymmetric extensions of the KdV equation, introducing an N=8 super-KdV system with a novel Poisson bracket structure.
Contribution
It presents a new N=8 super-KdV system based on division algebras and defines its Poisson structure via a non-associative superconformal algebra.
Findings
Constructed N=1,2,4,8 super-KdV extensions
Introduced a global N=8 super-KdV system
Defined a Poisson bracket structure using non-associative algebra
Abstract
The division algebras R, C, H, O are used to construct and analyze the N=1,2,4,8 supersymmetric extensions of the KdV hamiltonian equation. In particular a global N=8 super-KdV system is introduced and shown to admit a Poisson bracket structure given by the "Non-Associative N=8 Superconformal Algebra".
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