ArticleOriginal scientific text
Title
Veronese webs for bihamiltonian structures of higher corank
Authors 1
Affiliations
- Division of Mathematical Methods in Physics, University of Warsaw, Hoża St. 74, 00-682 Warszawa, Poland
Bibliography
- J. F. Adams, Lectures on Lie groups, W. A. Benjamin, Inc., 1969.
- V. I. Arnold, Mathematical methods of classical mechanics, Springer-Verlag, 1978.
- A. V. Bolsinov, Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution, Izv. Akad. Nauk SSSR Ser. Mat. 55 (1991), No 1; English transl. in: Math. USSR-Izv. 38 (1992), 69-90.
- N. Bourbaki, Groupes et algèbres de Lie, VII,VIII, Hermann, 1975.
- N. Bourbaki, Groupes et algèbres de Lie, IX, Masson, 1982.
- S. S. Chern and P. A. Griffiths, An inequality for the rank of a web and webs of maximum rank, Ann. Scuola Norm. Sup. Pisa 5 (1978), 539-557.
- S. S. Chern and P. A. Griffiths, Abel's theorem and webs, Jahresber. Deutsch. Math.-Verein. 80 (1978), 13-110.
- A. T. Fomenko and A. S. Mishchenko, Euler equations in finite-dimensional Lie groups, Izv. Akad. Nauk SSSR Ser. Mat. 42 (1978), 396-416; English transl. in: Math USSR-Izv. 12 (1978).
- A. T. Fomenko, Integrability and nonintegrability in geometry and mechanics, Kluwer Academic Publishers, 1988.
- I. M. Gelfand and I. S. Zakharevich, Spectral theory for a pair of skew-symmetrical operators on
, Functional Anal. Appl. 23 (1989), 85-93. - I. M. Gelfand and I. S. Zakharevich, Webs, Veronese curves, and bihamiltonian systems, J. Funct. Anal. 99 (1991), 150-178.
- I. M. Gelfand and I. S. Zakharevich, On the local geometry of a bihamiltonian structure, in: The Gelfand mathematical seminars, 1990-1992, Birkhäuser, Boston, 1993, 51-112.
- I. M. Gelfand and I. S. Zakharevich, Webs, Lenard schemes, and the local geometry of bihamiltonian Toda and Lax structures, math.DG/9903080.
- I. S. Zakharevich, Kronecker webs, bihamiltonian structures, and the method of argument translation, math.SG/9908034.
- A. L. Onishchik and E. B. Vinberg, Lie groups and algebraic groups, Springer-Verlag, 1990.
- R. Steinberg, Invariants of finite reflection groups, Canad. J. Math. 12 (1960), 616-618.