Invariant Traces on Algebras
Guido Karrer · Proceedings of the American Mathematical Society · 1974
Certain properties of traces on a finite-dimensional associative algebra A lead to the definition of an element $t(A) \in {H^1}({\text {Out}}\;A,{C^\ast }),{C^\ast }$ being the multiplicative group of the center of A as Out A-module. It is shown that $t(A) = 0$ is equivalent to the existence of nondegenerate traces on A which are invariant under composition with all automorphisms of A. In particular, by means of Galois theory, $t(A) = 0$ is shown for a semisimple algebra A, whereas $t(A) e 0$ for certain group algebras.