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Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

A derivation is a sequence of steps, logical or computational, from one result to another. The word derivation comes from the word "derive." "Derivation" can also refer to a ...

A nonassociative algebra named after physicist Pascual Jordan which satisfies xy=yx (1) and (xx)(xy)=x((xx)y)). (2) The latter is equivalent to the so-called Jordan identity ...

The Killing form is an inner product on a finite dimensional Lie algebra g defined by B(X,Y)=Tr(ad(X)ad(Y)) (1) in the adjoint representation, where ad(X) is the adjoint ...

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...

A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

Let A be a C^*-algebra having no unit. Then A^~=A direct sum C as a vector spaces together with 1. (a,lambda)+(b,mu)=(a+b,lambda+mu). 2. mu(a,lambda)=(mua,mulambda). 3. ...

"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 ...

A radical integer is a number obtained by closing the integers under addition, multiplication, subtraction, and root extraction. An example of such a number is RadicalBox[7, ...

Given a commutative ring R, an R-algebra H is a Hopf algebra if it has additional structure given by R-algebra homomorphisms Delta:H->H tensor _RH (1) (comultiplication) and ...