About the solutions to the Witten–Dijkgraaf– Verlinde–Verlinde associativity equations and their Lie-algebraic and geometric properties
Authors:
- Anatolij K. Prykarpatski
Abstract
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.
- Record ID
- CUT534e11b7a05945faa7942bc5889ac8aa
- Publication categories
- ; ;
- Author
- Pages
- 57-67
- Other elements of collation
- Bibliografia (na s.) - 66-67; Bibliografia (liczba pozycji) - 22; Oznaczenie streszczenia - Abstr.
- Book
- Kielanowski Piotr, Piotr Kielanowski Odzijewicz Anatol, Anatol Odzijewicz Previato Emma Emma Previato (eds.): Geometric Methods in Physics XXXVII : Workshop and Summer School, Białowieża, Poland, 2018, Trends in Mathematics, 2019, Cham, Birkhäuser Verlag, Birkhäuser, ISBN 978-3-030-34072-8 (eBook)
- Keywords in English
- Witten–Dijkgraaf–Verlinde associativity equations, oriented associativity equations, Lax–Sato type vector field equations, Adler–Kostant–Symes scheme, Lie-algebraic analysis, compatible Hamiltonian flows
- DOI
- DOI:10.1007/978-3-030-34072-8_6 Opening in a new tab
- URL
- https://link.springer.com/chapter/10.1007/978-3-030-34072-8_6#citeas Opening in a new tab
- Related project
- Teoria równań i nierówności różniczkowych, układy dynamiczne na rozmaitościach, wybrane działy: analizy matematycznej topologii algebry i geometrii oraz probabilistyki teorii grafów i liczb. . Project leader at PK: , ,
Działalność statutowa - Language
- eng (en) English
- Score (nominal)
- 20
- Additional fields
- Indeksowana w: Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT534e11b7a05945faa7942bc5889ac8aa/
- URN
urn:pkr-prod:CUT534e11b7a05945faa7942bc5889ac8aa
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.