In the LieAlgebras package, the command DGsetup is used to initialize a Lie algebra -- that is, to define the basis elements for the Lie algebra and its dual and to store the structure constants for the Lie algebra in memory.  The first argument for LieAlgebraData is a Lie algebra data structure which contains the structure constants in a standard format used by the LieAlgebras package.

The command LieAlgebraData(LieAlgebraName) returns the Lie algebra data structure for the Lie algebra with the name LieAlgebraName.  Thus, this command acts formally as the inverse of the command DGsetup.

This command can be used to paste a Lie algebra constructed in one Maple worksheet into another worksheet.

The command LieAlgebraData is part of the DifferentialGeometry:-LieAlgebras package.  It can be used in the form LieAlgebraData(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-LieAlgebraData(...).

$\mathrm{with}\left(\mathrm{DifferentialGeometry}\right)\:$$\mathrm{with}\left(\mathrm{LieAlgebras}\right)\:$

$L≔\mathrm{\_DG}\left(\left[\left[''LieAlgebra''\,\mathrm{Ex1}\,\left[3\right]\right]\,\left[\left[\left[1\,2\,1\right]\,1\right]\,\left[\left[2\,3\,2\right]\,1\right]\right]\right]\right)$

$L≔\left[\left[\mathrm{e1}\,\mathrm{e2}\right]\=\mathrm{e1}\,\left[\mathrm{e2}\,\mathrm{e3}\right]\=\mathrm{e2}\right]$

$\mathrm{DGsetup}\left(L\right)$

$\mathrm{Lie\; algebra:\; Ex1}$

$\mathrm{recoverL}≔\mathrm{LieAlgebraData}\left(\mathrm{Ex1}\right)$

$\mathrm{recoverL}≔\left[\left[\mathrm{e1}\,\mathrm{e2}\right]\=\mathrm{e1}\,\left[\mathrm{e2}\,\mathrm{e3}\right]\=\mathrm{e2}\right]$