38.14 AsUnitalSubalgebra

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.

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GAP 3.4.4
April 1997