Lie superheaps and their groupification

We introduce the notion of a Lie superheaps as a generalisation of Lie supergroups. We show that the well-known ‘groupification’ and ‘heapification’ functors generalise to the ambience of supergeometry. In particular, we show that there is an isomorphism between the categories of pointed Lie superheaps and Lie supergroups. To do this, we make extensive use of the functor of points.

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Publication Details

Journal
Bulletin of the Polish Academy of Sciences Mathematics
Published
2025-08-12
DOI
https://doi.org/10.4064/ba250420-6-8
Primary Topic
Advanced Topics in Algebra
Type
article
Field-Weighted Citation Impact
0.00
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article

Lie superheaps and their groupification

Andrew James Bruce
Bulletin of the Polish Academy of Sciences Mathematics
Advanced Topics in Algebra
article

Lie superheaps and their groupification

Andrew James Bruce
article en

Abstract

We introduce the notion of a Lie superheaps as a generalisation of Lie supergroups. We show that the well-known ‘groupification’ and ‘heapification’ functors generalise to the ambience of supergeometry. In particular, we show that there is an isomorphism between the categories of pointed Lie superheaps and Lie supergroups. To do this, we make extensive use of the functor of points.

Bulletin of the Polish Academy of Sciences Mathematics
Institute of Mathematics (PL), Polish Academy of Sciences (PL)
Openalex Percentile: Top 73%
Advanced Topics in Algebra
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Lie superheaps and their groupification — Andrew James Bruce · Bulletin of the Polish Academy of Sciences Mathematics (2025) | TGRS Research Map | TGRS