It has recently been observed that certain nonassociative algebras (called
"weakly nonassociative", WNA) determine, via a universal hierarchy of ordinary
differential equations, solutions of the KP hierarchy with dependent variable
in an associative subalgebra (the middle nucleus). We recall central results
and consider a class of WNA algebras for which the hierarchy of ODEs reduces to
a matrix Riccati hierarchy, which can be easily solved. The resulting solutions
of a matrix KP hierarchy then determine (under a rank 1 condition) solutions of
the scalar KP hierarchy. We extend these results to the discrete KP hierarchy.
Moreover, we build a bridge from the WNA framework to the Gelfand-Dickey
formulation of the KP hierarchy.Comment: 16 pages, second version: LaTeX problem with L's in section 5
resolved, third version: example 2 in section 3 added, some minor
corrections, forth version: a few small changes and corrections. Proceedings
of the workshop Algebra, Geometry, and Mathematical Physics, Lund, October,
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