Search Results for ""

Computer algebra is a diffuse branch of mathematics done with computers that encompasses both computational algebra and analysis.

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 abstract algebra concerned with results valid for many different kinds of spaces. Modules are the basic tools used in homological algebra.

An involutive algebra is an algebra A together with a map a|->a^* of A into A (a so-called involution), satisfying the following properties: 1. (a^*)^*=a. 2. (ab)^*=b^*a^*. ...

The root lattice of a semisimple Lie algebra is the discrete lattice generated by the Lie algebra roots in h^*, the dual vector space to the Cartan subalgebra.

A left Hilbert Algebra A whose involution is an antilinear isometry is called a unimodular Hilbert algebra. The involution is usually denoted xi|->xi^*.

If A is a graded module and there exists a degree-preserving linear map phi:A tensor A->A, then (A,phi) is called a graded algebra. Cohomology is a graded algebra. In ...

A local Banach algebra is a normed algebra A=(A,|·|_A) which satisfies the following properties: 1. If x in A and f is an analytic function on a neighborhood of the spectrum ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

"The" Jacobi identity is a relationship [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0,, (1) between three elements A, B, and C, where [A,B] is the commutator. The elements of a Lie algebra ...