Abstract
We study certain extensions of the Adler map on Grassmann algebras \(\Gamma(n)\) of order \(n\). We consider a known Grassmann-extended Adler map and under the assumption that \(n=1\), obtain a commutative extension of the Adler 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 by regarding it as a discrete dynamical system.
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Notes
Objects used in this paper arise in the study of spectral problems in soliton theory.
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Acknowledgments
The authors thank Vadim Kolesov for his comments.
Funding
This research started while S. Konstantinou-Rizos visited Heriot-Watt University in January 2019 and the University of Essex on an International Visiting Fellowship in November 2019. The research of S. Konstantinou-Rizos was supported by a grant from the Russian Science Foundation (Project No. 20-71-10110).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 179-187 https://doi.org/10.4213/tmf10045.
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Adamopoulou, P., Konstantinou-Rizos, S. & Papamikos, G. Integrable extensions of the Adler map via Grassmann algebras. Theor Math Phys 207, 553–559 (2021). https://doi.org/10.1134/S0040577921050019
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DOI: https://doi.org/10.1134/S0040577921050019