Algebraic loop structures on algebra comultiplications
In this paper, we study the algebraic loop structures on the set of Lie algebra comultiplications. More specifically, we investigate the fundamental concepts of algebraic loop structures and the set of Lie algebra comultiplications which have inversive, power-associative and Moufang properties depen...
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-07-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2019-0060 |
| _version_ | 1830177277420240896 |
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| author | Lee Dae-Woong |
| author_facet | Lee Dae-Woong |
| author_sort | Lee Dae-Woong |
| collection | DOAJ |
| description | In this paper, we study the algebraic loop structures on the set of Lie algebra comultiplications. More specifically, we investigate the fundamental concepts of algebraic loop structures and the set of Lie algebra comultiplications which have inversive, power-associative and Moufang properties depending on the Lie algebra comultiplications up to all the possible quadratic and cubic Lie algebra comultiplications. We also apply those notions to the rational cohomology of Hopf spaces. |
| first_indexed | 2024-12-17T19:22:21Z |
| format | Article |
| id | doaj.art-7b5731b5b9fb4a63a1ba78eb6023734f |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T19:22:21Z |
| publishDate | 2019-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-7b5731b5b9fb4a63a1ba78eb6023734f2022-12-21T21:35:29ZengDe GruyterOpen Mathematics2391-54552019-07-0117174275710.1515/math-2019-0060math-2019-0060Algebraic loop structures on algebra comultiplicationsLee Dae-Woong0Department of Mathematics, and Institute of Pure and Applied Mathematics, Chonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do, 54896, Republic of KoreaIn this paper, we study the algebraic loop structures on the set of Lie algebra comultiplications. More specifically, we investigate the fundamental concepts of algebraic loop structures and the set of Lie algebra comultiplications which have inversive, power-associative and Moufang properties depending on the Lie algebra comultiplications up to all the possible quadratic and cubic Lie algebra comultiplications. We also apply those notions to the rational cohomology of Hopf spaces.https://doi.org/10.1515/math-2019-0060lie algebra comultiplicationperturbationalgebraic loopinversive propertypower-associativitymoufang propertyeilenberg-maclane spacecohomology algebraprimary 17b70secondary 16t0555p4520n05 |
| spellingShingle | Lee Dae-Woong Algebraic loop structures on algebra comultiplications Open Mathematics lie algebra comultiplication perturbation algebraic loop inversive property power-associativity moufang property eilenberg-maclane space cohomology algebra primary 17b70 secondary 16t05 55p45 20n05 |
| title | Algebraic loop structures on algebra comultiplications |
| title_full | Algebraic loop structures on algebra comultiplications |
| title_fullStr | Algebraic loop structures on algebra comultiplications |
| title_full_unstemmed | Algebraic loop structures on algebra comultiplications |
| title_short | Algebraic loop structures on algebra comultiplications |
| title_sort | algebraic loop structures on algebra comultiplications |
| topic | lie algebra comultiplication perturbation algebraic loop inversive property power-associativity moufang property eilenberg-maclane space cohomology algebra primary 17b70 secondary 16t05 55p45 20n05 |
| url | https://doi.org/10.1515/math-2019-0060 |
| work_keys_str_mv | AT leedaewoong algebraicloopstructuresonalgebracomultiplications |