Permutability of characters on algebras
Let \(A\) be a subalgebra of \(M_n(F)\) where \(F\) is a field. \(A\) has permutable trace if the traces \(\text{tr}(abc)\) and \(\text{tr}(bac)\) are equal for any matrices \(a,b,c\in A\). The authors prove the following main results: i) Let the characteristic of \(F\) be either zero or \(p\) and \(n<2p\). Then \(A\) has permutable trace if and only if \(A/J(A)\) is commutative (\(J(A)\) is the Jacobson radical of \(A\)); ii) Let the trace form on \(A\), defined by \((a,b)=\text{tr}(ab)\) be non-degenerate. Then the trace is permutable if and only if \(A/J(A)\) is commutative; iii) Let the characteristic of \(F\) be non zero. Then \(A\) has permutable Brauer character if and only if \(A/J(A)\) is commutative.
scientific article; zbMATH DE number 1054048