## Tbilisi Mathematical Journal

- Tbilisi Math. J.
- Volume 5, Issue 2 (2012), 3-16.

### Sage computations of $\mathfrak{sl}_2(k)$-Levi extensions

Pilar Benito and Daniel de-la-Concepción

#### Abstract

In 2010, Snolb [9] studied the structure of nilpotent Lie algebras admitting a Levi extension. As a corollary of the results therein, it is shown that the classes of characteristically nilpotent or filiform Lie algebras do not admit Levi extensions. The paper ends by asking for the possibility of finding series of nilpotent Lie algebras in arbitrary dimension not being abelian or Heisenberg and allowing such extensions. Our goal in this work is to present computational examples of this type of algebras by using Sage software. In the case of nilpotent Lie algebras admitting $\mathfrak{sl}_2(k)$ as Levi factor special constructions will be given by means of Sage routines based on transvections over $\mathfrak{sl}_2(k)$-irreducible modules.

#### Note

Supported by the Spanish Goverment project MTM2010-18370-C04-03.

#### Article information

**Source**

Tbilisi Math. J., Volume 5, Issue 2 (2012), 3-16.

**Dates**

First available in Project Euclid: 12 June 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.tbilisi/1528768899

**Subjects**

Primary: 17B10: Representations, algebraic theory (weights) 17B30: Solvable, nilpotent (super)algebras 68W30: Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]

Secondary: 17B05: Structure theory

**Keywords**

Lie algebra Levi factor nilpotent Lie algebra simple and semisimple Lie algebra representation transvection

#### Citation

Benito, Pilar; de-la-Concepción, Daniel. Sage computations of $\mathfrak{sl}_2(k)$-Levi extensions. Tbilisi Math. J. 5 (2012), no. 2, 3--16. https://projecteuclid.org/euclid.tbilisi/1528768899