Search Results for ""

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

The double covering group of the (linear) symplectic group.

A hyper-Kähler manifold can be defined as a Riemannian manifold of dimension 4n with three covariantly constant orthogonal automorphisms I, J, K of the tangent bundle which ...

A change of coordinates matrix, also called a transition matrix, specifies the transformation from one vector basis to another under a change of basis. For example, if ...

The four following types of groups, 1. linear groups, 2. orthogonal groups, 3. symplectic groups, and 4. unitary groups, which were studied before more exotic types of groups ...

A diffeomorphism is a map between manifolds which is differentiable and has a differentiable inverse.

The finite simple groups of Lie-type. They include four families of linear simple groups: PSL(n,q) (the projective special linear group), PSU(n,q) (the projective special ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

A complex manifold for which the exterior derivative of the fundamental form Omega associated with the given Hermitian metric vanishes, so dOmega=0. In other words, it is a ...

A map F from R^n to R^n is area-preserving if m(F^(-1)(A))=m(A) for every subregion A of R^n, where m(A) is the n-dimensional measure of A. A linear transformation is ...