Computing faithful representations for nilpotent Lie algebras

JOURNAL OF ALGEBRA

卷:322

Article

Burde, Dietrich²  Eick, Bettina³  de Graaf, Willem¹ 

[1] Univ Trent, Dipartimento Matemat, I-38050 Trento, Italy

[2] Univ Vienna, Fak Math, A-1090 Vienna, Austria

[3] TU Braunschweig, Inst Computat Math, D-31806 Braunschweig, Germany

关键词: Nilpotent Lie algebras;    Faithful modules;    Computational methods;   

DOI  :  10.1016/j.jalgebra.2009.04.041

来源: Elsevier

【 摘 要 】

We describe various methods to determine a faithful representation of small dimension for a finite-dimensional nilpotent Lie algebra over an arbitrary field. We apply our methods to finding bounds for the smallest dimension mu(g) of a faithful g-module for some nilpotent Lie algebras g. In particular, we introduce an infinite family of filiform nilpotent Lie algebras f(n) of dimension n over Q and conjecture that mu(f(n)) > n + 1 holds. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free