Results 141 to 150 of about 164,410 (186)

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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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

Differential forms in computational algebraic geometry

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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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 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
openaire   +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 ...
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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

Differential algebra (contravariant analytic methods in differential geometry)

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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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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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).
openaire   +2 more sources