Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$(A,\hspace{0.55542pt}{\cdot }\hspace{1.111pt},\omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mspace width="0.55542pt" /> <mo>·</mo> <mspace width="1.111pt" /> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> be a simple n-Lie Poisson algebra over a field of zero characteristic, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ 1 \in A$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>∈</mo> <mi>A</mi> </mrow> </math></EquationSource> </InlineEquation>. Then we prove that the n-Lie algebra <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$A^{[1]}/(A^{[1]}\cap Z)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>A</mi> <mrow> <mo stretchy="false">[</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </msup> <mo stretchy="false">/</mo> <mrow> <mo stretchy="false">(</mo> <msup> <mi>A</mi> <mrow> <mo stretchy="false">[</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </msup> <mo>∩</mo> <mi>Z</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is simple, where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$A^{[1]}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>A</mi> <mrow> <mo stretchy="false">[</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> denotes the derived n-Lie ideal and Z is the center of n-Lie algebra <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$(A,\omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.

Simple n-Lie Poisson algebras

期刊论文
发表日期：

2026年4月9日

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Farukh Mashurov

摘要

Let $(A,\hspace{0.55542pt}{\cdot }\hspace{1.111pt},\omega )$ $(A, \cdot, ω)$ be a simple n-Lie Poisson algebra over a field of zero characteristic, $ 1 \in A$ $1 \in A$ . Then we prove that the n-Lie algebra $A^{[1]}/(A^{[1]}\cap Z)$ $A^{[1]} / (A^{[1]} \cap Z)$ is simple, where $A^{[1]}$ $A^{[1]}$ denotes the derived n-Lie ideal and Z is the center of n-Lie algebra $(A,\omega )$ $(A, ω)$ .