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Every finite-dimensional Lie algebra of characteristic p=0 has a faithful finite-dimensional representation.

If A is a normed algebra, a net {e_i} in A is called an approximate identity for A if sup_(i)|e_i|<infty and if for each a in A, e_ia->a and ae_i->a. Though this definition ...

An operator Gamma=sum_(i=1)^me_i^Ru^(iR) on a representation R of a Lie algebra.

Let A be a unital C^*-algebra, then an element u in A is called co-isometry if uu^*=1.

Every finite-dimensional Lie algebra of characteristic p!=0 has a faithful finite-dimensional representation.

A nonassociative algebra obeyed by objects such as the Lie bracket and Poisson bracket. Elements f, g, and h of a Lie algebra satisfy [f,f]=0 (1) [f+g,h]=[f,h]+[g,h], (2) and ...

A simple root of a Lie algebra is a positive root that is not the sum of two positive roots.

An algebra in which the associator (x,x,x)=0. The subalgebra generated by one element is associative.

Let A be a C^*-algebra, then a state is a positive linear functional on A of norm 1.

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y, (2) where x·y is vector multiplication which is assumed to be bilinear. Now define ...