Derivations of quasimatrix algebras
In [Sci. Pap. Coll. Gen. Educ., Univ. Tokyo 14, 157-164 (1964; Zbl 0203.048)] \textit{I. Murase} made the assertion that every derivation of a quasimatrix algebra Q is inner. His proof contained an error, and this result turned out to be false. On the basis of this paper, \textit{M. Abdeljaouad} [ibid. 21, 11-17 (1971; Zbl 0222.16033)] observed that every derivation of Q can actually be represented as the sum of an inner derivatioon and a derivation satisfying a certain additional condition. In [Mat. Zametki 24, 111-122 (1978; Zbl 0391.16023)] I described all derivations of a rather broad class of algebras close to matrix algebras. I assumed that the quasimatrix algebras belonged to this class. However, I. V. L'vov noted this is not so, and therefore the results of [op. cit.] do not yield a description of the derivations of quasimatrix algebras. The aim of the present paper is to describe all derivations of quasimatrix algebras.
scientific article; zbMATH DE number 4061449