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

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  • Dae-Woong Lee

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.

Suggested Citation

  • Dae-Woong Lee, 2013. "Algebraic Structures Based on a Classifying Space of a Compact Lie Group," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:508450
    DOI: 10.1155/2013/508450
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    References listed on IDEAS

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    1. Sahar Mohammad Abusalim & Mohd Salmi Md Noorani, 2013. "Fixed Point and Common Fixed Point Theorems on Ordered Cone b-Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, May.
    2. M. A. Kutbi & Jamshaid Ahmad & Nawab Hussain & Muhammad Arshad, 2013. "Common Fixed Point Results for Mappings with Rational Expressions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Sahar Mohammad Abusalim & Mohd Salmi Md Noorani, 2013. "Fixed Point and Common Fixed Point Theorems on Ordered Cone b‐Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. M. A. Kutbi & Jamshaid Ahmad & Nawab Hussain & Muhammad Arshad, 2013. "Common Fixed Point Results for Mappings with Rational Expressions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, June.
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