LieAlgebras[GeneralizedCenter] - find the generalized center of an ideal
Calling Sequences
GeneralizedCenter(S1, S2)
Parameters
S1 - a list of vectors defining a basis for an idealin a Lie algebra
S2 - (optional) list of vectors defining a basis for a subalgebra with
.Description
Examples
DifferentialGeometry, LieAlgebras, Center
Let be a Lie algebra, a subalgebra of , and an ideal with . Then the generalized center of with respect to is the ideal for all In particular, the generalized center of in is the inverse image of the center of the quotient algebra with respect to the canonical projection map .
A list of vectors defining a basis for the generalized center of in is returned. If the optional argument S2 is omitted, then the default is If the generalized center of in is trivial, then an empty list is returned.
The command GeneralizedCenter is part of the DifferentialGeometry:-LieAlgebras package. It can be used in the form GeneralizedCenter(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-GeneralizedCenter(...).
Example 1.
First initialize a Lie algebra.
Calculate the generalized center of [e1, e2] in the Lie algebra Alg1.
Calculate the generalized center of [e1, e4] in [e1, e2, e4, e5].
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