Research in Combinatorial Algebra

ZELMANOV，97-04132 我们专注于一些长期开放的问题，在代数和拓扑学有关的伯恩赛德问题。 第二个主题是窄群和李代数的研究，特别是，我们考虑了所谓的超共形代数和极大类的亲单幂群的分类。 建议的研究领域是组合代数。组合群论出现在大约一百年前，作为对某些 拓扑学中出现的无限群。这些年来，它或多或少地集中在以下三个主流问题上：（i）由生成者和关系者表示的群体，（ii）增长，（iii）伯恩赛德问题。从20世纪40年代开始，类似的问题已经被认为是无限维结合代数和李代数的深入研究。 这种扩大研究范围的动机是（a）内在需要的代数，特别是组合群论，（B）的应用功能分析，表示论，数论和（越来越多地在近年来）的数学物理。

ZELMANOV, 97-04132 We focus on a number of longstanding open problems in algebra and topology that are related to the Burnside Problem. A secondary topic is the study of narrow groups and Lie algebras, in particular, we consider the classification of the so called superconformal algebras and of pro-unipotent groups of maximal class. The area of proposed research is Combinatorial Algebra. Combinatorial Group Theory appeared about a hundred years ago as a study of certain infinite groups that arise in Topology. Throughout these years it has more or less focused on the following three mainstream problems : (i) groups presented by generators and relators, (ii) growth, (iii) the Burnside Problem. Starting with 1940s similar problems have been considered and intensively studied for infinite - dimensional associative and Lie algebras. This extension of scope of research was motivated (a) by the intrinsic needs of Algebra and in particular of Combinatorial Group Theory, (b) by applications to Functional Analysis, Representation Theory, Number Theory and (increasingly in recent years) by Mathematical Physics.