Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Peter Schauenburg

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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

Digital Object Identifier
doi:10.36045/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. doi:10.36045/bbms/1483671625. https://projecteuclid.org/euclid.bbms/1483671625


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