## Bulletin of the Belgian Mathematical Society - Simon Stevin

- Bull. Belg. Math. Soc. Simon Stevin
- Volume 23, Number 5 (2016), 769-777.

### 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.

#### Article information

**Source**

Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 5 (2016), 769-777.

**Dates**

First available in Project Euclid: 6 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1483671625

**Mathematical Reviews number (MathSciNet)**

MR3593574

**Zentralblatt MATH identifier**

06682401

#### Citation

Schauenburg, Peter. A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 5, 769--777. https://projecteuclid.org/euclid.bbms/1483671625