IJPAM: Volume 32, No. 4 (2006)

PRIMITIVE LIFTING IN
FREE NILPOTENT LIE ALGEBRAS

Zeynep Özkurt
Çukurova University
Department of Mathematics
Adana, 01330, TURKEY
e-mail: zyapti@mail.cu.edu.tr


Abstract.Let $F_{n}$ be the free nilpotent Lie algebra of rank $n$ and $L_{n,k}$ be the free $n$ generator nilpotent Lie algebra of class $k$. We show that, for $1\leq m\leq n$, every IA-system of $m$ elements of $L_{n,k}$ can be lifted to a primitive system of $m$ elements of $L_{n,k}$. In particular we establish primitive lifting in $L_{n,k}$ of a single element of $L_{n,k}$ modulo $\gamma _{c+1}(L_{n,k})$. We also present an automorphism of $F_{n}/\gamma_{c+1}(F_{n}) $ which cannot be lifted to an automorphisms of $F_{n}/\gamma _{c+1}(F_{n})^{\prime}$.

Received: September 19, 2006

AMS Subject Classification: 17B01, 17B40

Key Words and Phrases: primitive system, primitive lifting, automorphism

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 32
Issue: 4