Integrable extensions of Adler's map via Grassmann algebras

2020/12/30 by Panagiota Adamopoulou, Adamopoulou, P., S. Konstantinou-Rizos +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2012.15121

openalex publication_date 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study certain extensions of the Adler map on Grassmann algebras Γ(n) of order n. We consider a known Grassmann-extended Adler map, and assuming that n=1 we obtain a commutative extension of Adler's map in six dimensions. We show that the map satisfies the Yang--Baxter equation, admits three invariants and is Liouville integrable. We solve the map explicitly, viewed as a discrete dynamical system.

Related

• Entwining Yang-Baxter maps over Grassmann algebras
• Yang-Baxter algebras as convolution algebras: The Grassmannian case
• On the integrability of the transfer dynamics of non-involutive Yang-Baxter maps
• ℤ_N graded discrete Lax pairs and Yang-Baxter maps
• Entwining Yang-Baxter maps and integrable lattices