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

More Statistics

since 05 February 2011 :
View(s): 566 (15 ULiège)
Download(s): 47 (0 ULiège)

Claude Roger

About Lie-Rinehart superalgebras

(Volume 89 - Année 2020 — Articles)

DOI: 10.25518/0037-9565.9848

Article

Attached document(s)

original pdf file

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 of content

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

Image 10000000000002D2000001DCEC61E9574F1BE17A.png

Image 10000000000002CB0000023194D4E8619019938B.png

3. Lie-Rinehart superalgebras

Image 10000000000002CF00000132572E861C02A4A24C.png

Image 10000000000002C9000002BB66C64E54D95B2891.png

4. The purely odd supermanifold of dimension 0|n

Image 10000000000002CC00000097D17F80AD7ACD29EB.png

Image 10000000000002CF000003B4D11D8E5938F8C72B.png

Image 10000000000002C8000001754912DDA5C00A62C4.png

5. The case of Ṽ

Image 10000000000002CA00000142931F76919486E2B7.png

Image 10000000000002CC0000002EAD7ADDD433388804.png

Image 10000000000002D200000075D8712D8999EB977F.png

Image 10000000000002CD00000124FDA8AA2E3C58A01D.png

6. The case of ^V

Image 10000000000002CB0000023DD66419185CDA33AF.png

Image 10000000000002D90000039FEB5AEA8CD4F1D8D2.png

Image 10000000000002D2000003B6C0970454FC72B206.png

Image 10000000000002E3000000B04C9B447B66AF7985.png

7. Appendix

Image 10000000000002CB000001647EFA6EA6E1A8C3FB.png

Acknowledgments

Image 10000000000002CF0000006E2361697DAAD3302B.png

References

Image 10000000000002CE0000007BE0F9A2C6B242C4E5.png

Image 10000000000002CF000003B6151657B9D4948D3B.png

Image 10000000000002D10000007F91BF60A49A46FBA4.png

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

About: Claude Roger

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

Back to the table of contents

About Lie-Rinehart superalgebras

Attached document(s)

Abstract

Table of content

To cite this article

About: Claude Roger

Bulletin de la Société Royale des Sciences de Liège

Index