6 papers · 1 filter
Decompositions of Griess algebras beyond the OZ-setting
Jari Desmet, Louis Olyslager
To each VOA of strong CFT type, we associate a non-associative algebra which generalizes Griess algebras of One-Zero (OZ) VOAs. We compute the fusion law of Ising vectors in this a…
Groups of type over rings via TKK-algebras and their extremal elements
Seidon Alsaody, Jari Desmet
Over any commutative ring containing , we study Lie algebras of type that arise from the Tits--Kantor--Koecher (TKK) construction on a Brown algebra, a…
Automorphism groups of Matsuo algebras
Jari Desmet
In this paper, we determine the connected component of the automorphism group scheme of Matsuo algebras over fields of characteristic not .
Solid lines in axial algebras of Jordan type and Jordan algebras
Jari Desmet
We show that a primitive axial algebra of Jordan type is a Jordan algebra if and only if every -generated subalgebra is \emph{solid}, a notion introduced recen…
Non-associative Frobenius algebras of type
Jari Desmet
Recently, Maurice Chayet and Skip Garibaldi introduced a class of commutative non-associative algebras. In previous work, we gave an explicit description of these algebras for grou…
Non-associative Frobenius algebras of type with trivial Tits algebras
Jari Desmet
Very recently, Maurice Chayet and Skip Garibaldi have introduced a class of commutative non-associative algebras, for each simple linear algebraic group over an arbitrary field (wi…