38.13 AsSubalgebra

AsSubalgebra( 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 subalgebra S such that S has parent algebra A and is generated by the generators of U.

    gap> a:= [ [ 1, 0 ], [ 0, 0 ] ];;
    gap> b:= [ [ 0, 0 ], [ 0, 1 ] ] ;;
    gap> alg:= Algebra( Rationals, [ a, b ] );;
    gap> alg.name:= "alg";;
    gap> s:= Algebra( Rationals, [ a ] );
    Algebra( Rationals, [ [ [ 1, 0 ], [ 0, 0 ] ] ] )
    gap> AsSubalgebra( alg, s );
    Subalgebra( 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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