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algebra of manifolds

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  • algebra and algebraic structures — Generalized version of arithmetic that uses variables to stand for unspecified numbers. Its purpose is to solve algebraic equations or systems of equations. Examples of such solutions are the quadratic formula (for solving a quadratic equation)… …   Universalium

  • Curvature of Riemannian manifolds — In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous… …   Wikipedia

  • Exterior algebra — In mathematics, the exterior product or wedge product of vectors is an algebraic construction generalizing certain features of the cross product to higher dimensions. Like the cross product, and the scalar triple product, the exterior product of… …   Wikipedia

  • Poisson algebra — In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz law; that is, the bracket is also a derivation. Poisson algebras appear naturally in Hamiltonian mechanics, and are also central… …   Wikipedia

  • Treatise on Universal Algebra — A Treatise on Universal Algebra with applications (Eine Abhandlung über universale Algebra mit Anwendungen) ist ein Werk des Mathematikers und Philosophen Alfred North Whitehead aus dem Jahr 1898. In diesem Buch unternahm es Whitehead,… …   Deutsch Wikipedia

  • Maps of manifolds — A Morin surface, an immersion used in sphere eversion. In mathematics, more specifically in differential geometry and topology, various types of functions between manifolds are studied, both as objects in their own right and for the light they… …   Wikipedia

  • Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… …   Wikipedia

  • History of manifolds and varieties — The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic… …   Wikipedia

  • Graßmann-Algebra — Die Graßmann Algebra oder äußere Algebra eines Vektorraums V ist eine assoziative, schiefsymmetrisch graduierte Algebra mit Einselement. Sie ist – je nach Definition – Unteralgebra oder eine Faktoralgebra einer antisymmetrisierten Tensoralgebra… …   Deutsch Wikipedia

  • Äußere Algebra — Die Graßmann Algebra oder äußere Algebra eines Vektorraums V ist eine assoziative, graduierte Algebra mit Einselement. Sie ist – je nach Definition – eine Unteralgebra oder eine Faktoralgebra der Tensoralgebra und wird durch ΛV dargestellt. Die… …   Deutsch Wikipedia

  • Multilinear algebra — In mathematics, multilinear algebra extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concepts of p vectors and… …   Wikipedia

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