A majorization relation for a certain class of *-quivers with an orthogonality condition

In [1, 2, 3], *-algebras and *-categories over the field C of complex numbers were quasi-ordered with respect to the complexity of the structure of their *-representations with a majorization relation >-. A notion of *-wildness was also introduced there for an algebra (a category) if the algebra majorizes the *-algebra C* (F2)- In this paper, we discuss some methods for proving that an algebra is *-wild and obtain criteria for certain "standard" *-categories (ensembles with an orthogonality condition) to be *-wild.