Algebraic structures based on a classifying space of a compact Lie group
type: Item
instance of: scholarly article
title: Algebraic structures based on a classifying space of a compact Lie group
zbMATH Open document ID: 1292.55006
DOI: 10.1155/2013/508450
author: Dae-Woong Lee
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: The main purpose of this paper is to investigate the algebraic explanation based on a classifying space of the compact Lie group \(U(1)\) which is canonically isomorphic to the circle group \(S^1\). After constructing self-maps using the suspension structure, the author defines a useful commutator of self-maps on the suspension of a classifying space of the compact Lie group. He constructs the connected graded free Lie algebra structure by considering the rationally nontrivial indecomposable and decomposable generators of homotopy groups and the cohomology cup products. He shows that the homomorphic image of homology generators can be expressed in terms of the Lie brackets in rational homology. By using the Milnor-Moore theorem, he also investigates the concrete primitive elements as the images of the Hurewicz homomorphisms in the Pontrjagin algebra. The paper is well written and organized. The reviewer wonders why the author published the paper in this journal. It should be published in a journal related to topology.
Mathematics Subject Classification ID: 55R35
zbMATH DE Number: 6306956
zbMATH Keywords: classifying space of a compact Lie group
zbMATH Keywords: Pontrjagin algebra
zbMATH Keywords: Hurewicz map
zbMATH Keywords: rational homotopy
Wikidata QID: Q58916956
reviewed by: Cenap Özel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/508450
OpenAlex ID: W2023249584
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description: scientific article; zbMATH DE number 6306956