Research in Combinatorial Algebra

ZELMANOV，97-04132我们专注于代数和拓扑学中一些与伯恩赛德问题有关的长期悬而未决的问题。第二个主题是对窄群和李代数的研究，特别地，我们考虑了所谓的超共形代数和极大类的原酉群的分类。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，是对拓扑学中出现的某些无限群的研究。在这些年里，它或多或少地侧重于以下三个主流问题：(1)由生成者和关系者提出的群体，(2)增长，(3)伯恩赛德问题。从20世纪40年代开始，人们对无限维结合李代数和李代数的类似问题进行了深入的研究。这种研究范围的扩展是由于(A)代数特别是组合群论的内在需要，(B)泛函分析、表示理论、数论的应用，以及(近年来越来越多的)数学物理的应用。

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.