Linearization of algebraic structures via functor calculus

The classical correspondance between groups and Lie algebras has been extended in the literature to various varieties of loops by associating a suitable type of algebras with each of them, e.g. Mal'cev algebras with Moufang loops and Sabinin algebras with all loops, mostly by using geometric methods.

We will present the foundations of a new, algebraic (actually functor theoretic) approach allowing to construct analogous linearizations in a much broader context, consisting of a suitable linear operad associated with any semi-abelian category. This operad recovers the types of algebras previously associated with groups and numerous varieties of loops. Extending the classical Lazard correspondance and Baker-Campbell-Hausdorff (BCH) formula to this framework using polynomial functor theory instead of the exponential function is an ongoing project.

In the two previous talks on the subject the main tool of functor calculus and a commutator theory derived from it were discussed in length. In this talk we will review the main features of these topics before focussing on the construction of the before-mentioned operad associated with a semi-abelian category or, more specifically, semi-abelian variety of universal algebras. Also the new functor theoretic approach to the BCH formula and its possible extension to the latter framework will be sketched and illustrated by a Lazard type correspondance and explicit BCH formula for the first but already remarkably complex case of 2-divisible 2-nilpotent varieties.

举办单位：数学与统计学院

发 布 人：吴双 发布时间： 2018-05-16

发 布 人：吴双 发布时间： 2018-05-16

Manfred Hartl是法国Valenciennes大学数学系正教授；是群论、范畴代数领域的国际知名研究者；在IMRN、AIM、JA等著名杂志上发表有影响力的论文20余篇。自2017年秋季学期起，Hartl教授受聘我校长期外籍专家；依托研究团队为陈银副教授所在研究小组。