Polynomial Lie Algebras
Polynomial Lie Algebras
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多项式李代数
DOI：
10.1023/a:1021757609372
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发表时间：
2002
影响因子：
0.4
通讯作者：
D. Leykin
中科院分区：
文献类型：
--
作者：
V. Buchstaber;D. Leykin
引入并研究了一类特殊的无限维李代数，它们是多项式环上的有限维模。这类李代数称为多项式李代数。得到了一些分类结果。引入了环k[x1，…，xn]/(f1，…，fn)上的结合余代数结构，并在此基础上给出了函数孤立奇点不变量卷积矩阵的显式表达式。对于A、B、C、D和E6型的简单奇点，构造了由卷积矩阵定义的运动标架的结构多项式。
We introduce and study a special class of infinite-dimensional Lie algebras that are finite-dimensional modules over a ring of polynomials. The Lie algebras of this class are said to be polynomial. Some classification results are obtained. An associative co-algebra structure on the rings k[x1,...,xn]/(f1,...,fn) is introduced and, on its basis, an explicit expression for convolution matrices of invariants for isolated singularities of functions is found. The structure polynomials of moving frames defined by convolution matrices are constructed for simple singularities of the types A,B,C, D, and E6.