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Weyl algebra

Weyl 代数

本站译名 表示论与李理论 义项编号TS-1196

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Introduction to Representation Theory 封面

《Introduction to Representation Theory》 · 印刷第 8 页 Section 2.2 的域约定、第 9 页 Example 2.2.4(4) 的自由代数记号、第 17 页 Section 2.7「Examples of algebras」节首第 (1) 项(省略中间内容)

Let $k$ be a field. Unless stated otherwise, we will always assume that $k$ is algebraically closed, i.e., any nonconstant polynomial with coefficients in $k$ has a root in $k$. […] 4. The free algebra $A=k\langle x_1,\ldots,x_n\rangle$. A basis of this algebra consists of words in letters $x_1,\ldots,x_n$, and multiplication in this basis is simply the concatenation of words. […] The following two examples are among the simplest interesting examples of noncommutative associative algebras: (1) the Weyl algebra, $k\langle x,y\rangle/\langle yx-xy-1\rangle$;

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