半简单代数Nijenhuis算子和作为Nijenhuis流形的三维李群

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI:10.1134/S1061920825600758

E. Zhikhareva

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引用次数: 0

摘要

摘要本文的目的是反驳“只有半简单代数Nijenhuis算子存在的李代数是阿贝尔代数”的猜想。我们不仅提供了任意维的例子，而且还对三维李代数进行了分类，这些李代数在复情况和实情况下都允许这样的算子。作为一个副产品，我们得到了三维李群的列表，这些李群是左不变Nijenhuis流形。DOI 10.1134 / S1061920825600758

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

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

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.