About the solutions to the Witten—Dijkgraaf— Verlinde—Verlinde associativity equations and their Lie-algebraic and geometric properties
There is devised an algebraically feasible approach to investigating 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 mathematics. The main construction is based on a modified version of the Adler–Kostant–Symes scheme, applied to the Lie algebra of the loop diffeomorphism group of a torus and modified for the case of the Gauss–Manin displacement equations, depending on a spectral parameter. Their interpretation as characteristic equations for some system of the Lax–Sato type vector field equations made it possible to derive the determining separated Hamiltonian evolution equations for the related structure matrices, generating commutative and isoassociative algebras under consideration.
KeywordsWitten–Dijkgraaf–Verlinde–Verlinde associativity equations oriented associativity equations Lax–Sato type vector field equations Adler–Kostant–Symes scheme Lie-algebraic analysis compatible Hamiltonian flows.
Mathematics Subject Classification (2000)35A30 35G25 35N10 37K35 58J70 58J72 34A34.
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