Skew axial algebras of Monster type

Skew axets were first defined by McInroy and Shpectorov where they used the term of axets to classify shapes of an algebra. When they first submitted their paper, it was not known if skew axial algebras exist and now we will present such examples with axet X'(1 + 2). Looking at 2-generated primitive axial algebras of Monster type, we will be able to state and prove the classification of such algebras with axet X1(1 +2). We will conclude by looking at larger skew axets and give a suggestion on how one could extend the classification. (c) 2024 The Author. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).