Results 291 to 300 of about 281,620 (316)

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
openaire   +2 more sources

Power Geometry in Algebraic and Differential Equations

, 2013
Aleksandr Dmitrievich Bri︠u︡no
semanticscholar   +2 more sources

Algebraic Topology Via Differential Geometry

, 1988
In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required.
M. Karoubi, C. Leruste
semanticscholar   +2 more sources

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

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 ...
openaire   +2 more sources

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
semanticscholar   +2 more sources

Current Algebras, the Sugawara Model, and Differential Geometry

Journal of Mathematical Physics, 1970
The Lie algebra defined by the currents in the Sugawara model is defined in a way that is natural from the point of view of Lie transformation theory and differential geometry. Previous remarks that the Sugawara model is associated with a field-theoretical dynamical system on a Lie group manifold are made more precise and presented in a differential ...
openaire   +2 more sources

Algebraic geometry of Abel differential equation

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2012
Consider a system of differential equations \[ \dot{x}= -y + F(x,y), \qquad \dot{y}=x+G(x,y), \tag{\(*\)} \] where \(F\) and \(G\) are analytic functions without constant and linear terms. This system has a center at the origin if all the solutions around the origin are periodic.
Giat, Sh., Shelah, Y., Shikhelman, C., Yomdin, Y.   +3 more
openaire   +1 more source

Algebraic and Differential Geometry in Modern Optimization

2023
Stochastic optimization algorithms have become indispensable in modern machine learning. The developments of theories and algorithms of modern optimization also requires the application of tools from different methematical branches, such as algebraic and differential geometry.
openaire   +1 more source

Quantum Clifford algebra from classical differential geometry

Journal of Mathematical Physics, 2002
We show the emergence of Clifford algebras of nonsymmetric bilinear forms as cotangent algebras of Kaluza–Klein (KK) spaces pertaining to teleparallel space–times. These spaces are canonically determined by the horizontal differential invariants of Finsler bundles of the type, B′(M)→S(M), where B′(M) is the set of all the tangent frames to a ...
Vargas, Jose G., Torr, Douglas G.
openaire   +1 more source