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Closed and exact differential forms — In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form that is the exterior derivative of another … Wikipedia
De Rham cohomology — For Grothendieck s algebraic de Rham cohomology see Crystalline cohomology. In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic… … Wikipedia
Projective representation — In the mathematical field of representation theory, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to :PGL( V ,F) = GL( V ,F)/F lowast; where GL( V ,F) is the automorphism group of… … Wikipedia
Circle bundle — In mathematics, an (oriented) circle bundle is an oriented fiber bundle where the fiber is the circle , or, more precisely, a principal U(1) bundle. It is homotopically equivalent to a complex line bundle. In physics, circle bundles are the… … Wikipedia
Lie bialgebra — In mathematics, a Lie bialgebra is the Lie theoretic case of a bialgebra: its a set with a Lie algebra and a Lie coalgebra structure which are compatible. It is a bialgebra where the comultiplication is skew symmetric and satisfies a dual Jacobi… … Wikipedia

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