Construction of Elements

elt< L | r_1, r_2, ..., r_n > : AlgLie, RngElt, RngElt, ..., RngElt -> AlgLieElt

Given a Lie algebra L of dimension n over a ring R, and ring elements r_1, r_2, ..., r_n in R construct the element r_1 * e_1 + r_2 * e_2 + ... + r_n * e_n of L.

L ! Q : AlgLie, SeqEnum[RngElt] -> AlgLieElt

Given a Lie algebra L of dimension n and a sequence Q = [r_1, r_2, ..., r_n] of elements of the base ring R of L, construct the element r_1 * e_1 + r_2 * e_2 + ... + r_n * e_n of L.

Zero(L) : AlgLie -> AlgLieElt

L ! 0 : AlgLie, RngIntElt -> AlgLieElt

Create the zero element of the Lie algebra L.

Random(L) : AlgLie -> AlgLieElt

Given an Lie algebra L defined over a finite ring, return a random element.

BasisProduct(L, i, j) : AlgLie, RngIntElt, RngIntElt -> AlgLieElt

Return the product of the i-th and j-th basis element of L.

BasisProducts(L) : AlgLie -> [[ AlgLieElt ]]

Return the products of all basis elements of L as a sequence Q of n sequences of n elements of L, where n is the dimension of L. The element Q[i][j] is the product of the i-th and j-th basis elements.