Search Results for ""

Let A be any algebra over a field F, and define a derivation of A as a linear operator D on A satisfying (xy)D=(xD)y+x(yD) for all x,y in A. Then the set D(A) of all ...

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

The infinitesimal algebraic object associated with a Lie groupoid. A Lie algebroid over a manifold B is a vector bundle A over B with a Lie algebra structure [,] (Lie ...

The commutation operation [a,b]=ab-ba corresponding to the Lie product.

The multiplication operation corresponding to the Lie bracket.

Polypons are polyforms obtained from dividing a regular triangular grid into 30-30-120 triangles, illustrated above. The numbers of polypons with n=1, 2, ... components are ...

A reduced root system is a root system R satisfying the additional property that, if alpha in R, then the only multiples of alpha in R are +/-alpha.

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.

The structure constant is defined as iepsilon_(ijk), where epsilon_(ijk) is the permutation symbol. The structure constant forms the starting point for the development of Lie ...

Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...