On Lie semiheaps and ternary principal bundles

Andrew James Bruce

Archivum Mathematicum (2024)

  • Issue: 2, page 101-124
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Bruce, Andrew James. "On Lie semiheaps and ternary principal bundles." Archivum Mathematicum (2024): 101-124. <http://eudml.org/doc/299263>.

@article{Bruce2024,
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.},
author = {Bruce, Andrew James},
journal = {Archivum Mathematicum},
keywords = {heaps; semiheaps; principal bundles; group actions; generalised associativity},
language = {eng},
number = {2},
pages = {101-124},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On Lie semiheaps and ternary principal bundles},
url = {http://eudml.org/doc/299263},
year = {2024},
}

TY - JOUR
AU - Bruce, Andrew James
TI - On Lie semiheaps and ternary principal bundles
JO - Archivum Mathematicum
PY - 2024
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 2
SP - 101
EP - 124
AB - 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.
LA - eng
KW - heaps; semiheaps; principal bundles; group actions; generalised associativity
UR - http://eudml.org/doc/299263
ER -

References

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