论文标题
投影维度和通勤多样的还原性谎言代数
Projective dimension and commuting variety of a reductive Lie algebra
论文作者
论文摘要
多种还原谎言的通勤多样性代数$ \ mathfrak {g} $是$ \ mathfrak {g} \ times \ times \ mathfrak {g} $的基础定义的基础。在本说明中，证明该方案是正常的和Cohen-Macaulay。特别是，它的定义理想是主要的理想。实际上，该定理是由一个所谓的属性（P）引起的，该属性（P）是一个简单的代数。该属性说某些共同体学综合体是准确的。
The commuting variety of a reductive Lie algebra $\mathfrak{g}$ is the underlying variety of a well defined subscheme of $\mathfrak{g}\times\mathfrak{g}$. In this note, it is proved that this scheme is normal and Cohen-Macaulay. In particular, its ideal of definition is a prime ideal. As a matter of fact, this theorem results from a so called Property (P) for a simple Lie algebra. This property says that some cohomology complexes are exact.
