Let $A$ be a finite dimensional $K$-algebra (K a field) and $I$ a two-sided ideal of $A$. (if it helps we can assume that $A$ is a connected quiver algebra or a group algebra and $I$ a power of the Jacobson radical first). Then the split extension of $A$ by $I$ is the algebra $B=A \oplus I$ with multiplication $(a_1,i_i)(a_2,i_2)=(a_1 a_2, a_1 i_2+i_1 a_2+i_1 i_2)$.
Question: Is there an easy way to obtain the split extension $B$ as a $K$-algebra in GAP when given an algebra $A$ and ideal $I$?