Three Representation Types for Systems of Forms and Linear Maps

Abdullah Alazemi, Milica Anđelić, Carlos M. da Fonseca, Vyacheslav Futorny and Vladimir V. Sergeichuk
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Abdullah Alazemi: Department of Mathematics, Kuwait University, Safat 13060, Kuwait
Milica Anđelić: Department of Mathematics, Kuwait University, Safat 13060, Kuwait
Carlos M. da Fonseca: Department of Mathematics, Kuwait College of Science and Technology, Safat 13133, Kuwait
Vyacheslav Futorny: Department of Mathematics, University of São Paulo, São Paulo 05508, Brazil
Vladimir V. Sergeichuk: Institute of Mathematics, Tereshchenkivska 3, 01024 Kiev, Ukraine

Mathematics, 2021, vol. 9, issue 5, 1-12

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.

Keywords: representations of quivers; representations of mixed graphs; wild problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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