Identities of representations of Lie algebras and *-polynomial identities (Q1284655)

The authors study *-polynomial identities of the \(2n\times 2n\) matrix algebra \(M_{2n}(K,^*)\) with symplectic involution. The main result is a criterion for a *-polynomial in skew-symmetric variables of a special kind to be an identity. This result is also restated for weak identities of the natural \(2n\)-dimensional representation of the symplectic Lie algebra.