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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 160, Number 3, Pages 403–433
DOI: https://doi.org/10.4213/tmf6407
(Mi tmf6407)
 

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
Full-text PDF (679 kB) Citations (7)
References:
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
English version:
Theoretical and Mathematical Physics, 2009, Volume 160, Issue 3, Pages 1203–1228
DOI: https://doi.org/10.1007/s11232-009-0111-6
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6407
  • https://www.mathnet.ru/eng/tmf/v160/i3/p403
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:864
    Full-text PDF :363
    References:91
    First page:23
     
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