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Axial Algebras: Questions and Conjectures
I. Gorshkov, S. Shpectorov
Axial algebras are non-associative algebras generated by idempotents, called axes, whose adjoint action satisfies a fusion law. When this fusion law is graded, axes naturally lead…
Groups of generalized Moufang type and -graded algebras
Ilya Gorshkov
A pair is called a faithful odd transposition group if is a normal set of involutions generating the group and the product of any two distinct elements of has o…
Solid subalgebras in algebras of Jordan type half
I. Gorshkov, S. Shpectorov, A. Staroletov
The class of algebras of Jordan type was introduced by Hall, Rehren and Shpectorov in 2015 within the much broader class of axial algebras. Algebras of Jordan type are commutat…
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…