Nilpotent SQS-Skeins With Nilpotent Derived Sloops

Abstract

In [5], Gueizow gave an example of semiboolean SQS-skeins of nilpotent class $2$, all its derived sloops are Boolean “or” of nilpotence class $1$. In this paper, we give an example of nilpotent SQS-skein of class $2$ whose derived sloops are all of nilpotence class $2$. Guelzow [6] has also given a construction of semiboolean SQS-skeins of nilpotence class $n$ whose derived sloops are all of class $1$. As an extension result, we prove in the present paper the existence of nilpotent SQS-skeins of class $n$ all of whose derived sloops are nilpotent of the same class $n$; for any positive integer $n$.