Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1990Publisher:JSTORJournal:Journal of the American Mathematical Society, volume 3, page 257 (issn: 0894-0347,

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Authors: George Lusztig;

doi: 10.2307/1990988 , 10.1090/s0894-0347-1990-1013053-9

Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras

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Abstract

0.1. An important role in the theory of modular representations is played by certain finite dimensional Hopf algebras u over Fp (the field with p elements, p = prime). Originally, u was defined (Curtis [3]) as the restricted enveloping algebra of a "simple" Lie algebra over Fp For our purposes, it will be more convenient to define u as follows. Let us fix an indecomposable positive definite symmetric Cartan matrix

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