Involve: A Journal of Mathematics

  • Involve
  • Volume 7, Number 5 (2014), 647-655.

A not-so-simple Lie bracket expansion

Julie Beier and McCabe Olsen

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Abstract

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.

Article information

Source
Involve, Volume 7, Number 5 (2014), 647-655.

Dates
Received: 14 May 2013
Revised: 3 February 2014
Accepted: 3 March 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513733726

Digital Object Identifier
doi:10.2140/involve.2014.7.647

Mathematical Reviews number (MathSciNet)
MR3245841

Zentralblatt MATH identifier
1342.17015

Subjects
Primary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras

Keywords
Lie algebra toroidal algebra

Citation

Beier, Julie; Olsen, McCabe. A not-so-simple Lie bracket expansion. Involve 7 (2014), no. 5, 647--655. doi:10.2140/involve.2014.7.647. https://projecteuclid.org/euclid.involve/1513733726


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References

  • A. Borel, Essays in the history of Lie groups and algebraic groups, History of Mathematics 21, American Math. Soc. and London Math. Soc., 2001.
  • K. H. Lum, “A presentation of toroidal algebras as homomorphic images of G.I.M. algebras”, Comm. Algebra 26:12 (1998), 4051–4063.
  • G. Lusztig, Introduction to quantum groups, Progress in Mathematics 110, Birkhäuser, Boston, 1993.