LieAlgebraName - Maple Help

LieAlgebraData[LieAlgebraName] - convert an array of structure constants to a Lie algebra data structure

Calling Sequence

Parameters

LieAlgebraName   - name or string, the name of a Lie algebra

Description

 • 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(...).

Examples

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

Example 1.

First we initialize a 3-dimensional Lie algebra called Ex1.

 > $L≔\mathrm{_DG}\left(\left[\left["LieAlgebra",\mathrm{Ex1},\left[3\right]\right],\left[\left[\left[1,2,1\right],1\right],\left[\left[2,3,2\right],1\right]\right]\right]\right)$
 ${L}{≔}\left[\left[{\mathrm{e1}}{,}{\mathrm{e2}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e3}}\right]{=}{\mathrm{e2}}\right]$ (2.1)
 > $\mathrm{DGsetup}\left(L\right)$
 ${\mathrm{Lie algebra: Ex1}}$ (2.2)

LieAlgebraData gives us back the Lie algebra data structure for the Lie algebra Ex1.  We can paste the output of LieAlgebraData into another worksheet.

 Ex1 > $\mathrm{recoverL}≔\mathrm{LieAlgebraData}\left(\mathrm{Ex1}\right)$
 ${\mathrm{recoverL}}{≔}\left[\left[{\mathrm{e1}}{,}{\mathrm{e2}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e3}}\right]{=}{\mathrm{e2}}\right]$ (2.3)