Notes on Super Projective Modules (Journal Article)
Morye, Archana S.
Notes on Super Projective Modules (Journal Article) - New Delhi , 2023 - 1226-1238p. - Indian Journal of Pure and Applied Mathematics , Volume 54: Number 4, December 2023 .
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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.
0019-5588
Free supermodules| Super projective modules| Superspace
Notes on Super Projective Modules (Journal Article) - New Delhi , 2023 - 1226-1238p. - Indian Journal of Pure and Applied Mathematics , Volume 54: Number 4, December 2023 .
***______________***
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.
0019-5588
Free supermodules| Super projective modules| Superspace