Results 281 to 290 of about 275,517 (307)

Differential forms in computational algebraic geometry [PDF]

Proceedings of the 2007 international symposium on Symbolic and algebraic computation, 2007
We give a uniform method for the two problems #CCC and #ICC of counting connected and irreducible components of complex algebraic varieties, respectively. Our algorithms are purely algebraic, i.e., they use only the field structure of C. They work efficiently in parallel and can be implemented by algebraic circuits of polynomial depth, i.e., in ...
Peter Bürgisser, Peter Scheiblechner
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Noncommutative differential geometry of matrix algebras

Journal of Mathematical Physics, 1990
The noncommutative differential geometry of the algebra Mn (C) of complex n×n matrices is investigated. The role of the algebra of differential forms is played by the graded differential algebra C(sl(n,C),Mn (C))=Mn (C)⊗Λsl(n,C)*,sl(n,C) acting by inner derivations on Mn (C).
Dubois-Violette, Michel, Kerner, Richard, Madore, John   +2 more
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Geometry of Differential Polynomial Functions, II: Algebraic Curves

American Journal of Mathematics, 1993
Let \({\mathcal F}\) be a differential field of characteristic zero with derivation \(\delta\), and let \({\mathcal C}\) be its field of constants. Assume that both fields are algebraically closed. In this paper and its sequels, the author studies differential polynomial functions on schemes \(X\) over \({\mathcal F}\) and their applications to the ...
A. Buium
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Differential geometry on Grassmann algebras

Letters in Mathematical Physics, 1976
H. C. Lee [1] developed the analogue of Riemannian geometry on a real symplectic manifold — the fundamental skew two-form taking the place of the symmetric tensor. The usual Riemannian concepts do not adapt themselves very well, thus ‘curvature’ is represented by a tensor of the third rank and ‘Killing's equations’ now involve this ‘curvature tensor ...
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Differential algebra (contravariant analytic methods in differential geometry) [PDF]

Journal of Soviet Mathematics, 1980
The problems of developing the apparatus of differential-geometric investigations based on the calculus of differential operators on bundles of semiholonomic jets of Ehresmann are considered.
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Differential Geometry of Quantum States, Observables and Evolution

Quantum Physics and Geometry, 2019
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analysed from this perspective, the relevant ...
Florio M. Ciaglia, Alberto Ibort, G. Marmo   +2 more
semanticscholar   +1 more source

Topological algebras and abstract differential geometry

Journal of Mathematical Sciences, 1999
The notions of connection and curvature on principal sheaves, with structural sheaf the sheaf of groups \({\mathcal G}{\mathcal L}(n, {\mathcal A})\), are studied where \({\mathcal A}\) is a sheaf of unital, commutative and associative algebras. Suitable topological algebras provide concrete models of principal sheaves for which an abstract Frobenius ...
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Algebraic geometry of Abel differential equation

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2012
A solution $$y(x)$$ of an Abel differential equation $$(1) \ y^{\prime }=p(x)y^2 + q(x) y^3$$ is called “closed” on
Clara Shikhelman, Y. Yomdin, Y. Shelah, Sh. Giat   +3 more
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An algebraic model of almost transitive differential geometry

Mathematical Notes, 1993
The author develops an interesting algebraic model for the theory of \(G\)- structures whose Lie algebra of infinitesimal automorphisms is transitive. Some ideas of the author's approach are analogous to the theory of filtered Lie algebras described by \textit{V. W. Guillemin} and \textit{S. Sternberg} [Bull. Am. Math. Soc.
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Noncommutative geometry with graded differential Lie algebras

Journal of Mathematical Physics, 1997
Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the Connes–Lott prescription of noncommutative geometry, differs from that, however, by the implementation of unitary
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