Representations of exceptional simple Jordan superalgebras of characteristic 3. (English) Zbl 1069.17011
Let \(B\) be one of Jordan superalgebras \(B(1,2),\, B(4,2)\) and \(J=H_3(B)\) the Jordan superalgebra of \(3\time 3\) Hermitian matrices over \(B\). It is assumed that the basic field \(k\) has characteristic 3. It is shown that every irreducible unital Jordan \(J\)-supermodule is either regular of its opposite. Moreover every unital Jordan \(J\)-supermodule is completely reducible and every unital Jordan superalgebra containing \(J\) as a unital superalgebra admits a graded Kronecker factorization.
Reviewer: Vyacheslav A. Artamonov (Moskva)
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