Notes on Super Projective Modules

Archana S. Morye (), Aditya Sarma Phukon () and V. Devichandrika ()
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Archana S. Morye: University of Hyderabad
Aditya Sarma Phukon: University of Hyderabad
V. Devichandrika: University of Hyderabad

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 4, 1226-1238

Abstract: Abstract Projective modules are a link between geometry and algebra as established by the theorem of Serre-Swan. In this paper, we define the super analog of projective modules and explore this link in the case of some particular super geometric objects. We consider the tangent bundle over the supersphere and show that the module of vector field over a supersphere is a super projective module over the ring of supersmooth functions. Also, we discuss a class of super projective modules that can be constructed from a projection map on modules defined over the ring of supersmooth functions over superspheres.

Keywords: Free supermodules; Super projective modules; Superspace; Primary: 17A70; Secondary: 16D40; 16W50; 17C70; 16W55 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00336-4

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