Resultant as the determinant of a Koszul complex |
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Authors: | A S Anokhina A Yu Morozov Sh R Shakirov |
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Institution: | 1. Institute for Theoretical and Experimental Physics, Moscow, Russia 2. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia
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Abstract: | The determinant is a very important characteristic of a linear map between vector spaces. Two generalizations of linear maps are intensively used in modern theory: linear complexes (nilpotent chains of linear maps) and nonlinear maps. The determinant of a complex and the resultant are then the corresponding generalizations of the determinant of a linear map. It turns out that these two quantities are related: the resultant of a nonlinear map is the determinant of the corresponding Koszul complex. We give an elementary introduction into these notions and relations, which will definitely play a role in the future development of theoretical physics. |
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