Witt代数的r元组交换簇  

Commuting variety of r-tuples over the Witt algebra

作　　者：姚裕丰[1] 张雅静 YAO Yufeng;ZHANG Yajing(Department of Mathematics,Shanghai Maritime University,Shanghai 201306,China)

机构地区：[1]上海海事大学数学系,上海201306

出　　处：《华东师范大学学报（自然科学版）》2021年第3期1-7,共7页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11771279,11671138,12071136)。

摘　　要：设g是特征大于3的代数闭域上的Witt代数,r是大于等于2的整数.Witt代数的r元组交换簇是g中互相交换的r元组的集合.对比Ngo在2014年关于典型李代数的工作,证明了Witt代数的r元组交换簇C_(r)(g)是可约的,共有p-1/2个不可约分支,且不是等维的;确定了所有不可约分支及其维数.特别地,Cr(g)既不是正规的也不是Cohen-Macaulay.这些结果不同于典型李代数sl2相应的结果.Let g be the Witt algebra over an algebraically closed field of characteristic p>3,and r∈Z≥2.The commuting variety C_(r)(g)of r-tuples over g is defined as the collection of all r-tuples of pairwise commuting elements in g.In contrast with Ngo’s work in 2014,for the case of classical Lie algebras,we show that the variety C_(r)(g)is reducible,and there are a total of p-1/2 irreducible components.Moreover,the variety C_(r)(g)is not equidimensional.All irreducible components and their dimensions are precisely determined.In particular,the variety C_(r)(g)is neither normal nor Cohen-Macaulay.These results are different from those for the case of classical Lie algebra,sl_(2).

关 键 词：WITT代数 不可约分支 维数 r元组交换簇 正规簇 

分 类 号：O151.26[理学—数学]