On Lie semiheaps and ternary principal bundles
| Autor: | Bruce, Andrew James |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Archivum Mathematicum, vol. 60 (2024), issue 2, pp. 101-124 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.5817/AM2024-2-101 |
| Popis: | We introduce the notion of a Lie semiheap as a smooth manifold equipped with a para-associative ternary product. For a particular class of Lie semiheaps we establish the existence of left-invariant vector fields. Furthermore, we show how such manifolds are related to Lie groups and establish the analogue of principal bundles in this ternary setting. In particular, we generalise the well-known `heapification' functor to the ambience of Lie groups and principal bundles. Comment: 18 pages. Typos and editing artifacts were corrected, and the results of the paper are extended. The notion of left-invariant vector fields is now included. Comments are still welcomed |
| Databáze: | arXiv |
| Externí odkaz: |
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