Results 271 to 280 of about 6,286 (306)

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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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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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 ...
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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
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

Differential forms in algebraic geometry

2011
Before considering more general spaces we shall first discuss (1) the r-dimensional projective space Π r . In this space we shall consider a homogeneous coordinate system (Z0, Z1, ... , Z r ). Let U α be that part of Π r in which Z α ≠ 0. In U α we may then introduce non-homogeneous coordinates zαi = Zι/Zα (ι≠α).
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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.
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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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Numerical Algebraic Geometry and Differential Equations

2014
In this paper we review applications of numerical algebraic geometry to differential equations. The techniques we address are direct solution, bootstrapping by filtering, and continuation and bifurcation. We review differential equations systems with multiple solutions and bifurcations.
Wenrui Hao, Bei Hu, Andrew J. Sommese
openaire   +1 more source

On initials and the fundamental theorem of tropical partial differential algebraic geometry

Journal of Symbolic Computation, 2023
Sebastian Falkensteiner, François Boulier, Zeinab Toghani   +2 more
exaly  

Convex Algebraic Geometry of Curvature Operators

SIAM Journal on Applied Algebra and Geometry, 2021
Renato G Bettiol, Mario Kummer
exaly