About the solutions to the Witten–Dijkgraaf– Verlinde–Verlinde associativity equations and their Lie-algebraic and geometric properties / Anatolij K. Prykarpatski // W: Geometric Methods in Physics ... więcej

About the solutions to the Witten–Dijkgraaf– Verlinde–Verlinde associativity equations and their Lie-algebraic and geometric properties / Anatolij K. Prykarpatski // W: Geometric Methods in Physics XXXVII : Workshop and Summer School, Białowieża, Poland, 2018 [Dokument elektroniczny] / eds. Piotr Kielanowski, Anatol Odzijewicz, Emma Previato. – Cham : Birkhäuser, 2019. – (Trends in Mathematics, ISSN 2297-024X). – S. 57-67. – Tryb dostępu: https://link.springer.com/chapter/10.1007/978-3-030-34072-8_6#citeas. – Bibliogr. 22 poz., Abstr. – doi: 10.1007/978-3-030-34072-8_6. – ISBN 978-3-030-34072-8 (eBook). – ISBN 978-3-030-34071-1

There is devised an algebraically feasible approach to investigatingsolutions to the oriented associativity equations, related with commutativeand isoassociative algebras, interesting for applications ... więcej

There is devised an algebraically feasible approach to investigatingsolutions to the oriented associativity equations, related with commutativeand isoassociative algebras, interesting for applications in the quantum de-formation theory and in some other fields of mathematics. The main con-struction 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 andmodified for the case of the Gauss–Manin displacement equations, dependingon a spectral parameter. Their interpretation as characteristic equations forsome system of the Lax–Sato type vector field equations made it possible toderive the determining separated Hamiltonian evolution equations for the re-lated structure matrices, generating commutative and isoassociative algebrasunder consideration.