The structure of alternative superbimodules (Q1910282)

The main purpose of the paper under review is to describe the alternative superbimodules of semisimple alternative superalgebras over an algebraically closed field of characteristic different from 2 and 3. The main results are: (i) If the superalgebra does not contain a supersubalgebra of type \((M_1 (F), M_1 (F))\) in its decomposition into prime ideals, then the superbimodules are merely alternative bimodules and their description can be obtained from \textit{R. D. Schafer} [Trans. Am. Math. Soc. 72, 1-17 (1952; Zbl 0046.03503)]. (ii) For the superalgebra \((M_1 (F), M_1(F))\) the author constructs a family of superbimodules which gives a complete list of the irreducible superbimodules.