## Journal of Generalized Lie Theory and Applications

### Contractions of 3-Dimensional Representations of the Lie Algebra $\mathfrak{sl}(2)$

#### Abstract

A theory of grading preserving contractions of representations of Lie algebras has been developed. In this theory, grading of the given Lie algebra is characterized by two sets of parameters satisfying a derived set of equations. Here we introduce a list of resulting 3-dimensional representations for the $\mathbb{Z}_3$-grading of the $\mathfrak{sl}(2)$ Lie algebra.

#### Article information

Source
J. Gen. Lie Theory Appl., Volume 6 (2012), 6 pages.

Dates
First available in Project Euclid: 15 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1505440831

Digital Object Identifier
doi:10.4303/jglta/G110902

Mathematical Reviews number (MathSciNet)
MR2954626

Zentralblatt MATH identifier
1254.17026

#### Citation

Smotlacha, Jan; Chadzitaskos, Goce. Contractions of 3-Dimensional Representations of the Lie Algebra $\mathfrak{sl}(2)$. J. Gen. Lie Theory Appl. 6 (2012), 6 pages. doi:10.4303/jglta/G110902. https://projecteuclid.org/euclid.jglta/1505440831