XXXVII Workshop on Geometric Methods in Physics 1-7.07.2018
VII School on Geometry and Physics 25-29.06.2018

Anatolij Prykarpatski

On the geometric structure of the WDVV associativity equations and their solutions

In this Letter I devise an algebraically feasible approach to in-
vestigating solutions to the oriented associativity equations, related with
commutative and isoassociative algebras, interesting for applications in
the quantum deformation theory and in some other fields of mathemat-
ics. The construction is based on a version of the Adler-Kostant-Symes
scheme, applied to the Lie algebra of the loop di¤eomorphism group of a
torus and modified for the case of the Gauss-Manin displacement equa-
tions, depending on a spectral parameter. Their interpretation as char-
actersitic equatiuons for some system of the Lax-Sato type vector fieldeld
equations made it possible to derive the determining separated Hamil-
tonian evolution equations for the related structure matrices, generating
commutative and isoassociative algebras under regard.

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