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Abstrakty
Linear operators on function and abstract algebras are considered and their consistency with an arbitrary subset or an ideal is studied. Then the consistency concept is formulated for general Poisson brackets in commutative algebras.
Wydawca
Czasopismo
Rocznik
Tom
Strony
233--244
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
- Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1, 00-661 Warsaw, Poland
Bibliografia
- [1] N. Aronszajn, Subcartesian and subriemanian spaces, Notices Amer. Math. Soc. 14 (1967) 111.
- [2] A. Frölicher, A. Kriegl, Linear Spaces and Differentiation Theory, J. Wiley and Sons, Chichester, (1988).
- [3] Ch. D. Marshall, Calculus on subcartesian spaces, J. Diff. Geom. 10 (1977), 115-137.
- [4] M. A. Mostov, The differentiable space structures of Milnor classifying spaces, simplicial complex and geometric relations, J. Diff. Geom. 14 (1979), 255-293.
- [5] I. Satake, On generalization of the notion of manifold, Proc. Natl. Acad. Sci. 42 (1956), 359-363.
- [6] R. Sikorski, Abstract covariant derivative, Colloq. Math. 18 (1967), 251-271.
- [7] R. Sikorski, Differential modules, Colloq. Math. 24 (1971), 45-70.
- [8] D. Przeworska-Rolewicz, Algebraic Analysis, PWN, Warszawa/Reidel, Dordrecht, 1988.
- [9] D. Przeworska-Rolewicz, A characterization of algebraic derivative, Bull. Acad. Polon. Sci. 17 (1969), 11-13.
- [10] D. Przeworska-Rolewicz, Algebraic derivative and abstract differential equations, An. Acad. Brasil. Cien. 42 (1970), 403-409.
- [11] D. Przeworska-Rolewicz, Algebraic derivative and initial value problem, Bull. Acad. Polon. Sci. 20 (1972), 629-633.
- [12] G. Virsik, Right inverses of vector fields, J. Austral. Math. Soc. (Series A) 58 (1995), 411-420
- [13] J. Nestruev, Smooth Manifolds and Observables, Springer Verlag, New York 2003.
- [14] R. Penrose and W. Rindler, Spinors and Space-Time, Cambridge University Press, 1984.
- [15] J. E. Marsden, The hamiltonian formulation of classical field theory, Contemp. Math. 71 (1988), 221-235.
- [16] W.Waliszewski, Regular and coregular mappings of differential spaces, Ann. Polon. Math. 30 (1975), 263-281.
- [17] P. Multarzyński and Z. Żekanowski, On general hamiltonian dynamical systems in differential spaces, Demonstratio Math. 24 (1991), 539-555.
- [18] I. Vaisman, Lectures on the Geometry of Poisson Manifolds, Birkhäuser, 1994.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0021-0025