You're viewing this item in the new Europeana website. View this item in the original Europeana.

On some free semigroups, generated by matrices

Let $$ A=\left [ \begin {matrix} 1 & 2 \\ 0 & 1 \end {matrix} \right ],\quad B_{\lambda }=\left [ \begin {matrix} 1 & 0 \\ \lambda & 1 \end {matrix} \right ]. $$ We call a complex number $\lambda $ “semigroup free“ if the semigroup generated by $A$ and $B_{\lambda }$ is free and “free” if the group generated by $A$ and $B_{\lambda }$ is free. First families of semigroup free $\lambda $'s were desc…