On Lie semiheaps and ternary principal bundles. (English) Zbl 07830507
Summary: 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.
MSC:
| 20N10 | Ternary systems (heaps, semiheaps, heapoids, etc.) |
| 22E15 | General properties and structure of real Lie groups |
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