Zelensky O. Indexes of exponent matrices

The quivers of exponent matrices are simple laced and strongly connected. Properties of admissible matrices have been discovered. One class of the rigid quivers was established. It was proven that a rigid quiver can not have loops. Also it was proven that there is a Gorenstein matrix (0,1,2) - matrix E with a permutation ? for an arbitrary permutation ?= ?(E) without fixed elements. The condition of existence of a Gorenstein exponent matrix of the size m+n with diagonal block in the form of the given matrices for arbitrary two matrices of size m and n was established. A criterion of the equivalence for cyclic Gorenstein matrices was discovered.