通用代数的变形构造

Pub Date : 2024-04-22 DOI:10.1093/imrn/rnae077

David Bowman, Dora Puljić, Agata Smoktunowicz

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引用次数: 0

摘要

变形理论研究的问题之一是确定给定的关联代数可以变形为哪些代数。在本文中，我们研究了一个不同但相关的问题，即：对于给定的关联有限维 ${mathbb{C}}$ 代数 $A$，找出可以变形为 $A$ 的代数 $N$。我们开发了一种简单的方法来研究这个问题，这种方法可以产生联立和平面变形。作为这种方法的应用，我们回答了迈克尔-韦米斯（Michael Wemyss）关于收缩代数的变形的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Construction of Deformations to General Algebras

One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative finite-dimensional ${\mathbb{C}}$-algebra $A$, find algebras $N$, which can be deformed to $A$. We develop a simple method that produces associative and flat deformations to investigate this question. As an application of this method we answer a question of Michael Wemyss about deformations of contraction algebras.

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