Abstract:
Generators of the ring of invariants are found for $(n\times n)$-matrices over an infinite field of characteristic $p>n^2-1$. The result is analogous to the well-known Procesi's theorem in characteristic zero.
Citation:
A. N. Zubkov, “Matrix invariants over an infinite field of finite characteristic”, Sibirsk. Mat. Zh., 34:6 (1993), 68–74; Siberian Math. J., 34:6 (1993), 1059–1065
\Bibitem{Zub93}
\by A.~N.~Zubkov
\paper Matrix invariants over an infinite field of finite characteristic
\jour Sibirsk. Mat. Zh.
\yr 1993
\vol 34
\issue 6
\pages 68--74
\mathnet{http://mi.mathnet.ru/smj810}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1268158}
\zmath{https://zbmath.org/?q=an:0832.16023}
\transl
\jour Siberian Math. J.
\yr 1993
\vol 34
\issue 6
\pages 1059--1065
\crossref{https://doi.org/10.1007/BF00973469}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1993MQ34600007}
Linking options:
https://www.mathnet.ru/eng/smj810
https://www.mathnet.ru/eng/smj/v34/i6/p68
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A. M. Elishev, A. Ya. Belov, F. Razavinia, Yu Jie-Tai, Wenchao Zhang, “Polynomial automorphisms, quantization, and Jacobian conjecture related problems. II. Quantization proof of Bergman's centralizer theorem”, Algebra, geometriya i kombinatorika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 214, VINITI RAN, M., 2022, 107–126
A. M. Elishev, A. Ya. Belov, F. Razavinia, Yu Dzhi-Tai, Venchao Zheng, “Polinomialnye avtomorfizmy, kvantovanie i zadachi vokrug gipotezy Yakobiana. III. Avtomorfizmy, topologiya popolneniya i approksimatsiya”, Algebra, geometriya i kombinatorika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 215, VINITI RAN, M., 2022, 95–128
A. M. Elishev, A. Ya. Belov, F. Razavinia, Yu Dzhi-Tai, Venchao Zheng, “Polinomialnye avtomorfizmy, kvantovanie i zadachi vokrug gipotezy Yakobiana. IV. Approksimatsii polinomialnymi simplektomorfizmami”, Algebra, geometriya, differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 216, VINITI RAN, M., 2022, 153–171
A. M. Elishev, A. Ya. Belov, F. Razavinia, Yu Dzhi-Tai, Venchao Zheng, “Polinomialnye avtomorfizmy, kvantovanie i zadachi vokrug gipotezy Yakobiana. V. Gipoteza Yakobiana i problemy tipa Shpekhta i Bernsaida”, Algebra, geometriya, differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 217, VINITI RAN, M., 2022, 107–137
Wenchao Zhang, Roman Yavich, Alexei Belov-Kanel, Farrokh Razavinia, Andrey Elishev, Jietai Yu, “Polynomial Automorphisms, Deformation Quantization and Some Applications on Noncommutative Algebras”, Mathematics, 10:22 (2022), 4214
H. DERKSEN, V. MAKAM, “WEYL'S POLARIZATION THEOREM IN POSITIVE CHARACTERISTIC”, Transformation Groups, 26:4 (2021), 1241
Harm Derksen, Visu Makam, “Algorithms for orbit closure separation for invariants and semi-invariants of matrices”, Alg. Number Th., 14:10 (2020), 2791
Harm Derksen, Visu Makam, “Generating invariant rings of quivers in arbitrary characteristic”, Journal of Algebra, 489 (2017), 435
Domokos M., Kuzmin S.G., Zubkov A., “Rings of matrix invariants in positive characteristic”, Journal of Pure and Applied Algebra, 176:1 (2002), 61–80
A. N. Zubkov, “On a generalization of the Razmyslov-Procesi theorem”, Algebra and Logic, –
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