Bulletin de la Société Royale des Sciences de Liège - Volume 89 - Année 2020 Articles

About Lie-Rinehart superalgebras

Claude Roger,

Institut Camille Jordan, Université de Lyon, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France, roger@math.univ-lyon1.fr

Abstract

We extend to the superalgebraic case the theory of Lie-Rinehart algebras and work out some examples concerning the most popular samples of super manofilds

Keywords : supermanifolds, Lie-Rinehart algebras, Frölicher-Nijenhuis bracket, Nijenhius-Richardson bracket, Schouten-Nijenhius bracket

1. Introduction

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2. Construction of the enveloping algebra

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3. Lie-Rinehart superalgebras

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4. The purely odd supermanifold of dimension 0|n

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5. The case of Ṽ

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6. The case of ^V

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7. Appendix

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Acknowledgments

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References

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To cite this article

Claude Roger, «About Lie-Rinehart superalgebras», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 89 - Année 2020, Articles, 186- 197 URL : http://popups.ulg.be/0037-9565/index.php?id=9848.

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