Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Prykarpatski, A.K. (2019). About the solutions to the Witten–Dijkgraaf– Verlinde–Verlinde associativity equations and their Lie-algebraic and geometric properties. In: Kielanowski, P., Odzijewicz, A., Previato, E. (eds) Geometric Methods in Physics XXXVII. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-34072-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-34072-8_6
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-34071-1
Online ISBN: 978-3-030-34072-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)