<p>The notion of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-Novikov algebras was introduced recently as a generalization of Novikov and bicommutative algebras. It looks like <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-Novikov algebras have a richer structure than Novikov algebras. So, unlike Novikov algebras, they have a two-dimensional simple algebra for <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\delta =-1.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>δ</mi> <mo>=</mo> <mo>-</mo> <mn>1</mn> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> The present paper is dedicated to the study of three-dimensional <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-Novikov algebras for <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\delta \notin \big \{0,1\big \}.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>δ</mi> <mo>∉</mo> <mrow> <mo maxsize="1.2em" minsize="1.2em" stretchy="true">{</mo> </mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mrow> <mo maxsize="1.2em" minsize="1.2em" stretchy="true">}</mo> </mrow> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> The algebraic and geometric classifications of complex three-dimensional <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-Novikov algebras are given. As a corollary, we prove that there are no simple three-dimensional <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-Novikov algebras.</p>

The algebraic and geometric classification of $\delta $-Novikov algebras

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发表日期：

2025年11月7日

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Hani Abdelwahab,
Ivan Kaygorodov,
Roman Lubkov

摘要

The notion of $\delta $ $δ$ -Novikov algebras was introduced recently as a generalization of Novikov and bicommutative algebras. It looks like $\delta $ $δ$ -Novikov algebras have a richer structure than Novikov algebras. So, unlike Novikov algebras, they have a two-dimensional simple algebra for $\delta =-1.$ $δ = - 1 .$ The present paper is dedicated to the study of three-dimensional $\delta $ $δ$ -Novikov algebras for $\delta \notin \big \{0,1\big \}.$ $δ \notin {0, 1} .$ The algebraic and geometric classifications of complex three-dimensional $\delta $ $δ$ -Novikov algebras are given. As a corollary, we prove that there are no simple three-dimensional $\delta $ $δ$ -Novikov algebras.

The algebraic and geometric classification of \(\delta \)-Novikov algebras

摘要