义项 · Sense

universal highest weight module

泛最高权模

本站译名 表示论与李理论 义项编号TS-1369

英文别名
Verma module
中文别名
Verma 模;威尔玛模

外文出处

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Topology 封面

《Topology》 · 第 19 页 · Chapter 2,Section 2.4;印刷第 70 页,Chapter 5,Section 5.5

For each $\lambda \in k, \lambda \neq 0$ there is an (infinite dimensional) $U$-module $M(\lambda)$ with basis $m_0, m_1, m_2, \dots$... we can take $M(\lambda) = U / (U E + U (K - \lambda))$. The description makes it clear that $M(\lambda)$ has the following universal property: If $M$ is a $U$-module and $m \in M$ a vector with $E m = 0$ and $K m = \lambda m$, then there is a unique homomorphism of $U$-modules $\varphi \colon M(\lambda) \to M$ with $\varphi(m_0) = m$.

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