About Lie-Rinehart superalgebras

Claude Roger

doi:10.25518/0037-9565.9848

Bulletin de la Société Royale des Sciences de Liège

0037-9565 1783-5720

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Claude Roger

About Lie-Rinehart superalgebras

(Volume 89 - Année 2020 — Articles)

DOI: 10.25518/0037-9565.9848

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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

Table des matières

1. Introduction

2. Construction of the enveloping algebra

3. Lie-Rinehart superalgebras

4. The purely odd supermanifold of dimension 0|n

1. Introduction

Image 10000000000002C9000001A9F880508A78AECD2F.png

Image 10000000000002CE0000016CD1C318C8E780B458.png

2. Construction of the enveloping algebra

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Image 10000000000002CB0000023194D4E8619019938B.png

3. Lie-Rinehart superalgebras

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Image 10000000000002C9000002BB66C64E54D95B2891.png

4. The purely odd supermanifold of dimension 0|n

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Image 10000000000002CF000003B4D11D8E5938F8C72B.png

Image 10000000000002C8000001754912DDA5C00A62C4.png

5. The case of Ṽ

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Image 10000000000002CD00000124FDA8AA2E3C58A01D.png

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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Pour citer cet 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 : https://popups.uliege.be/0037-9565/index.php?id=9848.

A propos de : Claude Roger

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

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About Lie-Rinehart superalgebras

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Abstract

Table des matières

Pour citer cet article

A propos de : Claude Roger

Bulletin de la Société Royale des Sciences de Liège

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