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math.RA2020
Inner ideals and structurable algebras: Moufang sets, triangles and hexagons
Tom De Medts, Jeroen Meulewaeter
We construct Moufang sets, Moufang triangles and Moufang hexagons using inner ideals of Lie algebras obtained from structurable algebras via the Tits--Kantor--Koecher construction.…
math.RA2019
Decomposition algebras and axial algebras
Tom De Medts, Simon F. Peacock, Sergey Shpectorov +1
We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) Th…
math.RA2017
Structurable algebras of skew-dimension one and hermitian cubic norm structures
Tom De Medts
We study structurable algebras of skew-dimension one. We present two different equivalent constructions for such algebras: one in terms of non-linear isotopies of cubic norm struct…