Representations of exceptional simple alternative superalgebras of characteristic 3 (Q2782661)

The authors study representations of simple alternative superalgebras \(B(1,2)\) and \(B(2,4)\). The irreducible superbimodules and bimodules with \(J\)-admissible superinvolution over these superalgebras are classified. The authors prove that every unital \(B(4,2)\)-superbimo\-dule is completely reducible, and every unital \(B(1,2)\)-superbimodule with \(J\)-admissible superinvolution is also completely reducible. Moreover, some analogues of the Kronecker factorization theorem are proved. Namely, every alternative superalgebra (with \(J\)-admissible superinvolution) \(B\) that contains \(A=B(4,2)\) (\(A=B(1,2)\)) as a unital subsuperalgebra admits a graded Kronecker factorization \(B=A\widetilde\otimes U\) for a certain associative commutative superalgebra \(U\).