IJPAM: Volume 30, No. 1 (2006)

PRIMITIVE LIFTING OF SOME ELEMENTS IN
FREE NILPOTENT LIE ALGEBRAS

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


Abstract.Let $F_{n}$ be a free Lie algebra of rank $n$ and $\gamma _{c}(F_{n})$ the $c$-th term of the lower central series of $F_{n}$. We prove that for each $1\leq i,k\leq n$ and $m\geq 1,$ every element of $F_{n}/\gamma _{c}(F_{n})$ of the form $x_{i}+\left[ x_{i},x_{k}^{m}\right] $ can be lifted to a primitive element of $F_{n}$.

Received: May 27, 2006

AMS Subject Classification: 17B01, 17B40

Key Words and Phrases: primitive lifting, automorphism

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 1