Geodesic
On Lie semiheaps and ternary principal bundles
Archivum mathematicum, Tome 60 (2024) no. 2, pp. 101-124 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2024-2-101
Classification : 20N10, 22E15
Keywords: heaps; semiheaps; principal bundles; group actions; generalised associativity 
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Bruce, Andrew James. On Lie semiheaps and ternary principal bundles. Archivum mathematicum, Tome 60 (2024) no. 2, pp. 101-124. doi: 10.5817/AM2024-2-101

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