AsUnitalSubalgebra( A, U )
Let A be a parent algebra and U be a parent algebra or a subalgebra
with a possibly different parent algebra, such that the generators of U
are elements of A. AsSubalgebra
returns a new unital subalgebra S
such that S has parent algebra A and is generated by the generators
of U. If U or A do not contain the zero-th power of elements an
error is signalled.
gap> a:= [ [ 1, 0 ], [ 0, 0 ] ];; gap> b:= [ [ 0, 0 ], [ 0, 1 ] ];; gap> alg:= Algebra( Rationals, [ a, b ] );; gap> alg.name:= "alg";; gap> s:= UnitalAlgebra( Rationals, [ a ] ); UnitalAlgebra( Rationals, [ [ [ 1, 0 ], [ 0, 0 ] ] ] ) gap> AsSubalgebra( alg, s ); Subalgebra( alg, [ [ [ 1, 0 ], [ 0, 0 ] ], [ [ 1, 0 ], [ 0, 1 ] ] ] ) gap> AsUnitalSubalgebra( alg, s ); UnitalSubalgebra( alg, [ [ [ 1, 0 ], [ 0, 0 ] ] ] )Note that
Subalgebra
, UnitalSubalgebra
, AsSubalgebra
and
AsUnitalSubalgebra
are the only functions in which the name
Subalgebra
does not refer to the mathematical terms subalgebra and
superalgebra but to the implementation of algebras as subalgebras and
parent algebras.
GAP 3.4.4