A. Alazemi, M. Anđelić, C.M. da Fonseca, V. Futorny, V.V. Sergeichuk (2021) Three representation types for systems of forms and linear maps, Mathematics, Vol. 9, No. 455, 10.3390/math9050455
Abstract. We consider systems of bilinear forms and linear maps as representations of a graph with undirected and directed edges. Its vertices represent vector spaces; its undirected and directed edges represent bilinear forms and linear maps, respectively. We prove that if the problem of classifying representations of a graph has not been solved, then it is equivalent to the problem of classifying representations of pairs of linear maps or pairs consisting of a bilinear form and a linear map. Thus, there are only two essentially different unsolved classification problems for systems of forms and linear maps.