Algebras and Representation Theory

, Volume 7, Issue 1, pp 1–17

Presenting Schur Algebras as Quotients of the Universal Enveloping Algebra of gl2


  • Stephen Doty
    • Mathematical and Computer SciencesLoyola University Chicago
  • Anthony Giaquinto
    • Mathematical and Computer SciencesLoyola University Chicago

DOI: 10.1023/B:ALGE.0000019386.04383.f9

Cite this article as:
Doty, S. & Giaquinto, A. Algebras and Representation Theory (2004) 7: 1. doi:10.1023/B:ALGE.0000019386.04383.f9


We give a presentation of the Schur algebras SQ(2,d) by generators and relations, in fact a presentation which is compatible with Serre's presentation of the universal enveloping algebra of a simple Lie algebra. In the process we find a new basis for SQ(2,d), a truncated form of the usual PBW basis. We also locate the integral Schur algebra within the presented algebra as the analogue of Kostant's Z-form, and show that it has an integral basis which is a truncated version of Kostant's basis.

Schur algebraenveloping algebragenerators and relations
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© Kluwer Academic Publishers 2004