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A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

The application of characteristic p methods in commutative algebra, which is a synthesis of some areas of commutative algebra and algebraic geometry.

A measure algebra which has many properties associated with the convolution measure algebra of a group, but no algebraic structure is assumed for the underlying space.

The Gelfand-Naimark theorem states that each C^*-algebra is isometrically *-isomorphic to a closed *-subalgebra of the algebra B(H) consisting of all bounded operators acting ...

An anchor is the bundle map rho from a vector bundle A to the tangent bundle TB satisfying 1. [rho(X),rho(Y)]=rho([X,Y]) and 2. [X,phiY]=phi[X,Y]+(rho(X)·phi)Y, where X and Y ...

Three or more points P_1, P_2, P_3, ..., are said to be collinear if they lie on a single straight line L. A line on which points lie, especially if it is related to a ...

If mu=(mu_1,mu_2,...,mu_n) is an arbitrary set of positive numbers, then all eigenvalues lambda of the n×n matrix a=a_(ij) lie on the disk |z|<=m_mu, where ...

The classification theorem of finite simple groups, also known as the "enormous theorem," which states that the finite simple groups can be classified completely into 1. ...

Oriented spheres in complex Euclidean three-space can be represented as lines in complex projective three-space ("Lie correspondence"), and the spheres may be thought of as ...

A finite simple group of Lie-type. The following table summarizes the types of twisted Chevalley groups and their respective orders. In the table, q denotes a prime power and ...