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arXiv · 2404.17708

NL bialgebras

Zohreh Ravanpak
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Abstract

In this paper, we introduce the concept of (weak) NL bialgebras. These structures consist of a Lie bialgebra $(\g,[\cdot,\cdot],\delta)$ equipped with a Nijenhuis structure on the Lie algebra $(\g,[\cdot,\cdot])$, satisfying specific compatibility conditions. This construction is analogous to Poisson-Nijenhuis structures studied in the context of integrable systems. We further investigate NL bialgebras that generate a compatible hierarchy of bialgebras, both on the original Lie algebra and its deformed versions, through the Nijenhuis structure of any order. Additionally, we demonstrate that the underlying algebraic structure of a particular case of the Euler-top system is a weak NL bialgebra.

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Zohreh Ravanpak. 2024-04-26. NL bialgebras. https://doi.org/10.4310/atmp.251023014528

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