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Abstract <p> The aim of this paper is to disprove the conjecture that the only Lie algebras admitting semisimple algebraic Nijenhuis operators are Abelian ones. We do not only provide examples in arbitrary dimension but also classify three-dimensional Lie algebras which admit such an operator in both complex and real cases. As a byproduct, we obtain a list of three-dimensional Lie groups which are left-invariant Nijenhuis manifolds. </p> <p> <b> DOI</b> 10.1134/S1061920825600758 </p>

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Semisimple Algebraic Nijenhuis Operators and Three-Dimensional Lie Groups as Nijenhuis Manifolds

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • E. Zhikhareva

摘要

Abstract

The aim of this paper is to disprove the conjecture that the only Lie algebras admitting semisimple algebraic Nijenhuis operators are Abelian ones. We do not only provide examples in arbitrary dimension but also classify three-dimensional Lie algebras which admit such an operator in both complex and real cases. As a byproduct, we obtain a list of three-dimensional Lie groups which are left-invariant Nijenhuis manifolds.

DOI 10.1134/S1061920825600758