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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 508450, 7 pages
http://dx.doi.org/10.1155/2013/508450
Research Article

Algebraic Structures Based on a Classifying Space of a Compact Lie Group

Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do 561-756, Republic of Korea

Received 5 July 2013; Revised 10 September 2013; Accepted 20 September 2013

Academic Editor: Teoman Özer

Copyright © 2013 Dae-Woong Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We analyze the algebraic structures based on a classifying space of a compact Lie group. We construct the connected graded free Lie algebra structure by considering the rationally nontrivial indecomposable and decomposable generators of homotopy groups and the cohomology cup products, and we show 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, we also investigate the concrete primitive elements in the Pontrjagin algebra.