Critical polynomials related to generalized derivations
The authors [ibid. 342, 1--15 (2002; Zbl 1026.11030)] have shown that, if \(V\) is a vector space and \(T\) is a linear operator on \(V\) with minimal polynomial of degree \(n\), then, \[ \left[\frac{m(n-1)}{k} \right]+1 \] is a lower bound for the degree of the minimal polynomial of the \(k\)-derivation of \(T\) on \(\otimes^m V\). Also some correlations between generalized derivations and problems in additive number theory may be found there. In the present paper the authors study the structure of the linear operators \(T\), whose minimal polynomial of the \(k\)-derivation has degree precisely equal to the bound above.
scientific article; zbMATH DE number 1970628