Vol. 7, No. 5, 2014

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A not-so-simple Lie bracket expansion

Julie Beier and McCabe Olsen

Vol. 7 (2014), No. 5, 647–655

Lie algebras and quantum groups are not usually studied by an undergraduate. However, in the study of these structures, there are interesting questions that are easily accessible to an upper-level undergraduate. Here we look at the expansion of a nested set of brackets that appears in relations presented in a paper of Lum on toroidal algebras. We illuminate certain terms that must be in the expansion, providing a partial answer for the closed form.

Lie algebra, toroidal algebra
Mathematical Subject Classification 2010
Primary: 17B67
Received: 14 May 2013
Revised: 3 February 2014
Accepted: 3 March 2014
Published: 1 August 2014

Communicated by Robert W. Robinson
Julie Beier
Department of Mathematics
Earlham College
801 National Road West
Drawer 138
Richmond, IN 47374
United States
McCabe Olsen
Mercer University
Department of Mathematics
1400 Coleman Avenue
Macon, GA 31207
United States