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Minimal set of differential invariants of an extended loop group arising in fluid flows

Grant number: 18/21330-2
Support Opportunities:Research Grants - Visiting Researcher Grant - International
Duration: February 01, 2019 - July 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Alexandre Grichkov
Grantee:Alexandre Grichkov
Visiting researcher: Vladimir Grebenev
Visiting researcher institution: Siberian Branch of the Russian Academy of Sciences (SB RAS), Russia
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project is devoted to one of the problems that occupied the researchers working in the area of Lie algebras at the turn of the last century, one can identify with generating the minimal set of diýerential invariants for Lie (pseudo-)group actions. The fundamental basis theorem states that all diýerential invariants can be generated from a nite number of low order invariants by repeated invariant diýerentiation. This theorem rst formulated by Lie in the nite-dimensional Lie (pseudo-) groups, and then extended by Tresse to in nite dimensional Liepseudo-groups, states that the diýerential invariant algebra is nitely generated. The problem is to construct the minimal set of diýerential invariants for Lie (pseudo-) group actions. (AU)

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Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
GREBENEV, VLADIMIR N.; DEMENKOV, ANDREW G.; CHERNYKH, GENNADY G.; GRICHKOV, ALEXANDRE N.. Local equilibrium approximation in free turbulent flows: Verification through the method of differential constrains. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, v. 101, n. 9, . (18/21330-2)
GREBENEV, VLADIMIR N.; DEMENKOV, ANDREW G.; CHERNYKH, GENNADY G.; GRICHKOV, ALEXANDRE N.. Local equilibrium approximation in free turbulent flows: Verification through the method of differential constrains. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, . (18/21330-2)
GREBENEV, V. N.; GRICHKOV, A. N.; OBERLACK, M.; WACLAWCZYK, M.. Second-order invariants of the inviscid Lundgren-Monin-Novikov equations for 2d vorticity fields. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 72, n. 3, . (18/21330-2)
GREBENEV, V. N.; WACLAWDZYK, M.; ODERLACK, M.. Conformal invariance of the zero-vorticity Lagrangian path in 2D turbulence. Journal of Physics A-Mathematical and Theoretical, v. 52, n. 33, . (18/21330-2)

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