Cyclic Frobenius algebras

DOI10.4213/RM10096EarXiv2302.04104MaRDI QIDQ6080800

Alexander V. Mikhailov, V. M. Buchstaber

Publication date: 4 October 2023

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/2302.04104

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) General and miscellaneous (16B99)

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