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december 2016 A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra
Peter Schauenburg
Bull. Belg. Math. Soc. Simon Stevin 23(5): 769-777 (december 2016). DOI: 10.36045/bbms/1483671625

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.

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Peter Schauenburg. "A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra." Bull. Belg. Math. Soc. Simon Stevin 23 (5) 769 - 777, december 2016. https://doi.org/10.36045/bbms/1483671625

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Published: december 2016
First available in Project Euclid: 6 January 2017

zbMATH: 06682401
MathSciNet: MR3593574
Digital Object Identifier: 10.36045/bbms/1483671625

Rights: Copyright © 2016 The Belgian Mathematical Society

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Vol.23 • No. 5 • december 2016
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