Algebraic Structures Based on a Classifying Space of a Compact Lie Group
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 th...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/508450 |
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| _version_ | 1832556772906237952 |
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| author | Dae-Woong Lee |
| author_facet | Dae-Woong Lee |
| author_sort | Dae-Woong Lee |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bb1ac0241a4d46a7bc6a4947cf72e6c4 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bb1ac0241a4d46a7bc6a4947cf72e6c42025-02-03T05:44:26ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/508450508450Algebraic Structures Based on a Classifying Space of a Compact Lie GroupDae-Woong Lee0Department 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 KoreaWe 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.http://dx.doi.org/10.1155/2013/508450 |
| spellingShingle | Dae-Woong Lee Algebraic Structures Based on a Classifying Space of a Compact Lie Group Abstract and Applied Analysis |
| title | Algebraic Structures Based on a Classifying Space of a Compact Lie Group |
| title_full | Algebraic Structures Based on a Classifying Space of a Compact Lie Group |
| title_fullStr | Algebraic Structures Based on a Classifying Space of a Compact Lie Group |
| title_full_unstemmed | Algebraic Structures Based on a Classifying Space of a Compact Lie Group |
| title_short | Algebraic Structures Based on a Classifying Space of a Compact Lie Group |
| title_sort | algebraic structures based on a classifying space of a compact lie group |
| url | http://dx.doi.org/10.1155/2013/508450 |
| work_keys_str_mv | AT daewoonglee algebraicstructuresbasedonaclassifyingspaceofacompactliegroup |