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Automorphism groups of axial algebras
Ilya Gorshkov, Justin McInroy, Tendai Mudziiri Shumba +1
Axial algebras are a class of commutative non-associative algebras which have a natural group of automorphisms, called the Miyamoto group. The motivating example is the Griess alge…
On -generated axial algebras of Jordan type
Ravil Bildanov, Ilya Gorshkov
Axial algebras of Jordan type are a special type of commutative non-associative algebras. They are generated by idempotents whose adjoint operators have the minimal polynomial…
Axial view on pseudo-composition algebras and train algebras of rank 3
Ilya Gorshkov, Andrey Mamontov, Alexey Staroletov
We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompos…