Classification of almost monomial subalgebras of small codimension

Abstract: In this text, we study almost monomial subalgebras using LAGBI bases. We introduce the concept of a LAGBI base and present an algorithm for computing them. We then use this algorithm to find, and present in a table, all polynomial subalgebras with Frobenius number smaller than or equal to ten. We then prove that some patterns observed in this table hold. Lastly we give a proof of what properties isomorphic subalgebras must have and use this to find all polynomial subalgebras up to isomorphism with Frobenius number up to five.