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Notes on Super Projective Modules

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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.

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Acknowledgements

The third author is thankful to the faculty and the administrative unit of the institute of mathematical sciences (IMSc) for their warm hospitality during the preparation of the paper.

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Author notes

  1. Aditya Sarma Phukon and V. Devichandrika contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Statistics, University of Hyderabad, C R Rao Road, Hyderabad, Telangana, 500019, India

    Archana S. Morye, Aditya Sarma Phukon & V. Devichandrika

  2. Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr, Madison, WI, 53706, USA

    Archana S. Morye, Aditya Sarma Phukon & V. Devichandrika

Authors
  1. Archana S. Morye
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  2. Aditya Sarma Phukon
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  3. V. Devichandrika
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Correspondence to V. Devichandrika.

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Communicated by Indranil Biswas.

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Morye, A.S., Sarma Phukon, A. & Devichandrika, V. Notes on Super Projective Modules. Indian J Pure Appl Math 54, 1226–1238 (2023). https://doi.org/10.1007/s13226-022-00336-4

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