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arXiv · 1806.06340

Remarks on Mathieu-Zhao Subspaces of Commutative Associative Algebras and Vertex Algebras

Gaywalee Yamskulna
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Abstract

We introduce a notion of Mathieu-Zhao subspaces of vertex algebras. Among other things, we show that for a vertex algebra $V$ and its subspace $M$ that contains $C_2(V)$, $M$ is a Mathieu-Zhao subspace of $V$ if and only if the quotient space $M/C_2(V)$ is a Mathieu-Zhao subspace of a commutative associative algebra $V/C_2(V)$. As a result, one can study the famous Jacobian conjecture in terms of Mathieu-Zhao subspaces of vertex algebras. In addition, for a $CFT$-type vertex operator algebra $V$ that satisfies the $C_2$-cofiniteness condition, we classify all Mathieu-Zhao subspaces $M$ that contain $C_2(V)$.

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BibTeXRIS

Gaywalee Yamskulna. 2018-06-17. Remarks on Mathieu-Zhao Subspaces of Commutative Associative Algebras and Vertex Algebras. https://arxiv.org/abs/1806.06340

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