Invariant Theory and wheeled PROPs

We study the category of wheeled PROPs using tools from Invariant Theory. A typical example a PROP is mixed tensor algebra V=T(V)⊗T(V⋆), where T(V) on an n-dimensional vector space over field K characteristic 0. First we classify all ideals initial object Z in PROPs. show that non-degenerate sub-wheeled V are exactly subalgebras form VG G closed, reductive subgroup general linear group GL(V). When finite dimensional Hilbert space, similar description invariant tensors for action compact was given by Schrijver. also generalize theorem Procesi says trace rings satisfying n-th Cayley-Hamilton identity can be embedded n×n matrix ring commutative R. Namely, prove R⊗V K-algebra R if and only it satisfies certain relations.