38.8 Subalgebra

Subalgebra( A, gens )

returns the subalgebra of the algebra A generated by the elements in the list gens.

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

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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