The zero element of the Lie algebra L.
Given a Lie algebra L defined over a finite ring, a random element is returned.
Given a Lie algebra L of dimension n over a ring R, and ring elements r1, r2, ..., rn ∈R construct the element r1 * e1 + r2 * e2 + ... + rn * en of L.
Given a Lie algebra L of dimension n and a sequence Q = [r1, r2, ..., rn] of elements of the base ring R of L, the element r1 * e1 + r2 * e2 + ... + rn * en of L is constructed.
Returns the product of the i-th and j-th basis element of the Lie algebra L.
Rep: MonStgElt Default: "Dense"
Returns the products of all basis elements of the Lie algebra L.The optional parameter Rep may be used to specify the format of the result. If Rep is set to "Dense", the products are returned 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.
If Rep is set to "Sparse", the products are returned as a sequence Q containing quadruples (i, j, k, aijk) signifying that the product of the i-th and j-th basis elements is ∑k=1n aijk bk, where bk is the k-th basis element and n = dim(L).
Matrix Lie elements can be constructed using the functions below. For more information on constructing matrices see Section Construction of a Matrix.
Create the element of the matrix Lie algebra R of degree n whose entries are the n2 elements of the sequence L.
Diagonal matrix in the matrix Lie algebra L, given by the sequence Q of ring elements.
Scalar matrix in the matrix Lie algebra L, defined by the ring element r.