# A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra

Abstract : Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite dimension. In finite characteristic, the universal enveloping algebra of a restricted Lie algebra admits a quotient Hopf algebra which is finite-dimensional if the Lie algebra is. Rumynin has shown that suitably defined restricted Lie algebroids allow to define restricted universal enveloping algebras that are finitely generated projective if the Lie algebroid is. This note presents an alternative proof and possibly fills a gap that might, however, only be a gap in the author's understanding.
Type de document :
Pré-publication, Document de travail
2015
Domaine :

https://hal.archives-ouvertes.fr/hal-01175667
Contributeur : Peter Schauenburg <>
Soumis le : samedi 11 juillet 2015 - 12:18:39
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

### Identifiants

• HAL Id : hal-01175667, version 1
• ARXIV : 1505.02608

### Citation

Peter Schauenburg. A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra. 2015. 〈hal-01175667〉

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