Lie's correspondence for commutative automorphic formal loops
| Autor: | José M. Pérez-Izquierdo, A. Grishkov |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Pure mathematics Algebra and Number Theory Formal power series Automorphic L-function Simple Lie group 010102 general mathematics Formal group Jacquet–Langlands correspondence 010103 numerical & computational mathematics Hopf algebra 01 natural sciences Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Abelian group ANÉIS E ÁLGEBRAS NÃO ASSOCIATIVOS Commutative property Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | We develop Lie's correspondence for commutative automorphic formal loops, which are natural candidates for non-associative abelian groups, to show how linearization techniques based on Hopf algebras can be applied to study non-linear structures. Over fields of characteristic zero, we prove that the category of commutative automorphic formal loops is equivalent to certain category of Lie triple systems. An explicit Baker–Campbell–Hausdorff formula for these loops is also obtained with the help of formal power series with coefficients in the algebra of 3 by 3 matrices. Our formula is strongly related to the function ( e 2 s − e 2 t ) ( s + t ) 2 ( e 2 ( s + t ) − 1 ) . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|