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Diametral theory of algebraic surfaces and geometric theory of invariants of groups generated by reflections. III

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Abstract

We present the geometric theory of invariants of wild groups of skew symmetries in a real Euclidean space.

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References

  1. P. J. Olver, Applications of Lie Groups to Differential Equations, Springer (1986).

  2. E. B. Vinberg and V. L. Popov, “Theory of invariants,” in: VINITI Series in Contemporary Problems of Mathematics. Fundamental Trends [in Russian], Vol. 55, VINITI, Moscow (1989), pp. 137–309.

    Google Scholar 

  3. D. V. Alekseevskii, A. M. Vinogradov, and V. V. Lychagin, “Fundamental ideas and concepts of differential geometry,” in: VINITI Series in Contemporary Problems of Mathematics. Fundamental Trends,Vol. 28, VINITI (1988), pp. 5–298.

  4. L. S. Pontryagin, Continuous Groups [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  5. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

  6. I. M. Gel’fand and A. S. Mishchenko, “Quadratic forms over commutative group rings and K-theory,” Funkts. Anal. Prilozhen., 3, No. 4, 28–33 (1969).

    Google Scholar 

  7. S. S. Ryshkov and E. P. Baranovskii, “Classical methods of the theory of lattice packings,” Usp. Mat. Nauk, 34, No. 4, 4–63 (1979).

    MathSciNet  Google Scholar 

  8. R. Home, “Respectives on invariant theory: Schur duality, multiplicity—free actions and beyond,” Isr. Algebr. Geometry, 3 173–186 (1996).

    Google Scholar 

  9. W. Barth, “Two projective surfaces with many nodes admitting the symmetries of the icosahedron,” J. Algebr. Geometry, 3, 173–186 (1996).

    Google Scholar 

  10. V. F. Ignatenko, “Diametral theory of algebraic surfaces and geometric theory of invariants of groups generated by reflections. I,” Ukr. Mat. Zh., 50, No. 5, 639–653 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  11. V. F. Ignatenko, “Diametral theory of algebraic surfaces and geometric theory of invariants of groups generated by reflections. II,” Ukr. Mat. Zh., 50, No. 6, 792–802 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  12. V. F. Ignatenko, “Algebraic surfaces with an infinite set of planes of skew symmetry. I,” Ukr. Mat. Sb.,Issue 32, 47–60 (1989).

  13. V. F. Ignatenko, “On the geometric theory of invariants of groups generated by reflections,” in: VINITI Series in Problems of Geometry [in Russian], Vol. 21, VINITI, Moscow (1989), pp. 155–208.

    Google Scholar 

  14. V. F. Ignatenko, “Algebraic surfaces with an infinite set of skew symmetry planes. Manual arrangement of linear spans of four orbits of symmetry directions,” Trans. Amer. Math. Soc., 176, 27–51 (1996).

    MathSciNet  Google Scholar 

  15. V. F. Ignatenko, On One Method for the Construction of Infinite Groups of Skew Symmetry [in Russian], Dep. at Ukr. GNTB, No. 1744-Uk95, Simferopol (1995).

  16. V. F. Ignatenko, “On the contemporary state of the theory of invariants of infinite groups of skew symmetries,” in: Scientific Works of the Department of Mathematics [in Russian], Simferopol University, Simferopol (1997), pp. 54–56.

    Google Scholar 

  17. V. F. Ignatenko, “ Algebraic surfaces with an infinite set of planes of skew symmetry. II,” Ukr. Mat. Sb., Issue 34, 42–51 (1991).

  18. V. F. Ignatenko and A. I. Krivoruchko, Rings of Invariants of Special Groups of Skew Symmetries [in Russian], Dep. at Ukr. GNTB, No. 82-Uk98, Simferopol (1997).

  19. V. F. Ignatenko, Invariants of finite and infinite groups generated by reflections,” J. Math. Soc., 76, No. 3, 334–361 (1996).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Simferopol University, Simferopol

    V. F. Ignatenko

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  1. V. F. Ignatenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 10, pp. 1324–1340, October, 1998.

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Ignatenko, V.F. Diametral theory of algebraic surfaces and geometric theory of invariants of groups generated by reflections. III. Ukr Math J 50, 1513–1531 (1998). https://doi.org/10.1007/BF02513500

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  • DOI: https://doi.org/10.1007/BF02513500

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