Address: Department of Mathematics, The Computational Foundry, Swansea University Bay Campus, Fabian Way, Swansea, SA1 8EN
E-mail: andrewjamesbruce@googlemail.com
Abstract: 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.
AMSclassification: primary 20N10; secondary 22E15.
Keywords: heaps, semiheaps, principal bundles, group actions, generalised associativity.
DOI: 10.5817/AM2024-2-101