## Involve: A Journal of Mathematics

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

### A not-so-simple Lie bracket expansion

#### 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