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This article is cited in 7 scientific papers (total in 7 papers)
Resultant as the determinant of a Koszul complex
A. S. Anokhinaab, A. Yu. Morozova, Sh. R. Shakirovab a Institute for Theoretical and Experimental Physics, Moscow, Russia
b Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia
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.
Keywords:
resultant, Koszul complex, nonlinear algebra.
Received: 06.02.2009
Citation:
A. S. Anokhina, A. Yu. Morozov, Sh. R. Shakirov, “Resultant as the determinant of a Koszul complex”, TMF, 160:3 (2009), 403–433; Theoret. and Math. Phys., 160:3 (2009), 1203–1228
Linking options:
https://www.mathnet.ru/eng/tmf6407https://doi.org/10.4213/tmf6407 https://www.mathnet.ru/eng/tmf/v160/i3/p403
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