INVESTIGADORES
CAGLIERO Leandro Roberto
artículos
Título:
Faithful representations of minimal dimension of current Heisenberg Lie algebras
Autor/es:
L. CAGLIERO; N. ROJAS
Revista:
INTERNATIONAL JOURNAL OF MATHEMATICS
Editorial:
World Scientific Publishing
Referencias:
Año: 2008
ISSN:
0129-167X
Resumen:
Given a Lie algebra $g$ over a field of characteristic zero $k$,let $mu(g)=min{dim pi: pi ext{ is a faithful representation of }g}$.Let $h_{m}$ bethe Heisenberg Lie algebra of dimension $2m+1$ over $k$ and let$k[t]$ be the polynomial algebra in one variable. Given$minmathbb{N}$ and $pink[t]$, let $h_{m,p}=h_motimesk[t]/(p)$ be the current Lie algebra associated to $h_m$ and$k[t]/(p)$, where $(p)$ is the principal ideal in $k[t]$ generated by $p$.In this paper we prove that $ mu(h_{m,p}) = m deg p + leftlceil 2sqrt{deg p} ight ceil. $.
