Non-commutative graded algebras and their Hilbert series
Non-commutative graded algebras and their Hilbert series
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非交换分级代数及其希尔伯特级数
DOI：
10.1016/0021-8693(82)90104-1
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发表时间：
1982
影响因子：
0.9
通讯作者：
D. Anick
中科院分区：
文献类型：
--
作者：
D. Anick
本文开始发展非交换分次代数及其Hilbert级数的理论，它与已有的广泛的交换分次代数理论相平行。我们开始讨论“单项式的序理想”，它给我们这些代数的向量空间基。接下来我们发展了“弱被加数”的概念，这是一个子代数与代数之间的特殊关系，以及“强自由集”的概念。强自由集有许多类似于交换代数中正则序列的性质。我们讨论“组合自由”集，这是有用的构造许多前面的想法的例子。我们的结论与应用我们的结果代数拓扑表明，有一个有限的CW-复杂的只有9个正维细胞的循环空间有一个无理庞加莱级数。
This paper begins to develop a theory of non-commutative graded algebras and their Hilbert series which parallels the extensive already existing theory on commutative graded algebras. We begin with a discussion of “order ideals of monomials,” which give us vector space bases for these algebras. We develop next the concept of “weak summand,” which is a special relationship a subalgebra may have to an algebra, and the concept of “strongly free sets.” Strongly free sets have many properties which are analogous to the properties of regular sequences in commutative algebras. We discuss “combinatorially free” sets, which are useful for constructing examples of many of the preceding ideas. We conclude with an application of our results to algebraic topology by showing that there is a finite CW-complex with only nine positive-dimensional cells whose loop space has an irrational Poincaré series.