Growth, entropy and commutativity of algebras satisfying prescribed relations
Growth, entropy and commutativity of algebras satisfying prescribed relations
复制标题
满足规定关系的代数的增长、熵和交换性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Smoktunowicz
中科院分区：
文献类型：
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作者：
A. Smoktunowicz
1964年，Golod和Shafarevich发现，只要每个度的关系的个数满足一定的界，就存在满足这些关系的无穷维代数。这些代数被称为Golod-Shafarevich代数。本文根据定义关系的个数给出了Golod-Shafarevich代数象上增长函数的界。这扩展了Smoktunowicz和Bartholdi（Q J Math. doi：10.1093/qmath/hat 0052013）和Smoktunowicz（J Algebra 381：116-130，2013）的结果。构造代数的增长下界也得到了，允许各种增长函数的各种熵代数的建设。特别地，本文通过构造满足给定关系的具有次指数增长的代数来回答Drensky（A private communication，2013）的问题，在对每个度的生成关系的数量的温和假设下。也构造了不可数域上既没有多项式也没有指数增长的诣零代数的例子，回答了Zelmanov（2013）的一个问题。最近，在非交换奇点的研究中，出现了几个关于满足一定数量定义关系的代数的交换性的公开问题。此外，本文还解决了Donovan和Wemarty提出的一个这样的问题（Noncommutative deformations and flops，ArXiv：1309.0698v2 [math.AG]）。
In 1964, Golod and Shafarevich found that, provided that the number of relations of each degree satisfies some bounds, there exist infinitely dimensional algebras satisfying the relations. These algebras are called Golod–Shafarevich algebras. This paper provides bounds for the growth function on images of Golod–Shafarevich algebras based upon the number of defining relations. This extends results from Smoktunowicz and Bartholdi (Q J Math. doi:10.1093/qmath/hat0052013) and Smoktunowicz (J Algebra 381:116–130, 2013). Lower bounds of growth for constructed algebras are also obtained, permitting the construction of algebras with various growth functions of various entropies. In particular, the paper answers a question by Drensky (A private communication, 2013) by constructing algebras with subexponential growth satisfying given relations, under mild assumption on the number of generating relations of each degree. Examples of nil algebras with neither polynomial nor exponential growth over uncountable fields are also constructed, answering a question by Zelmanov (2013). Recently, several open questions concerning the commutativity of algebras satisfying a prescribed number of defining relations have arisen from the study of noncommutative singularities. Additionally, this paper solves one such question, posed by Donovan and Wemyss (Noncommutative deformations and flops, ArXiv:1309.0698v2 [math.AG]).
影响因子：
2.5
作者：
W. Donovan;M. Wemyss
通讯作者：
W. Donovan;M. Wemyss
限制增长的零代数
影响因子：
0.7
作者：
Lenagan T
通讯作者：
Lenagan T