Open AccessOn minimal faithful representations of a class of nilpotent lie algebras
Author(s) -
María Alvarez Alejandra,
Nadina Rojas
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2105671a
Subject(s) - mathematics , dimension (graph theory) , lie algebra , nilpotent , class (philosophy) , simple (philosophy) , pure mathematics , algebra over a field , discrete mathematics , philosophy , epistemology , artificial intelligence , computer science
In this work we consider 2-step nilradicals of parabolic subalgebras of the simple Lie algebra An and describe a new family of faithful nil-representations of the nilradicals na,c, a,c ? N. We obtain a sharp upper bound for the minimal dimension ?(na,c) and for several pairs (a,c) we obtain ?(na,c).