38.9 UnitalSubalgebra

UnitalSubalgebra( A, gens )

returns the unital subalgebra of the algebra A generated by the elements in the list gens. If A is not (known to be) unital then first it is checked that A really contains the zero-th power of elements.

    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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