Cyclic Frobenius algebras
Exactly Solvable and Integrable Systems
2023-02-09 v1 Mathematical Physics
math.MP
Rings and Algebras
Abstract
In this paper, we introduce the notion of cyclic Frobenius algebras (CF-algebras). Canonical structures of CF-algebras exist on associative and Poisson algebras. It turns out that the modern theory of integrable systems yields non-trivial examples of CF-algebras. In the theory of the KdV hierarchy there is a structure of CF-algebra which leads to explicit expressions for the first integrals of the N-th Novikov hierarchy, suitable for classical, non-Abelian and quantum cases.
Keywords
Cite
@article{arxiv.2302.04104,
title = {Cyclic Frobenius algebras},
author = {V. M. Buchstaber and A. V. Mikhailov},
journal= {arXiv preprint arXiv:2302.04104},
year = {2023}
}