I. Gorshkov

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20242026

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math.RA2026

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…

math.RA2026

Groups of generalized Moufang type and $Z_{2}$ -graded algebras

Ilya Gorshkov

A pair $(G, T)$ is called a faithful odd transposition group if $T$ is a normal set of involutions generating the group $G$ and the product of any two distinct elements of $T$ has o…

math.RA2024

On $3$ -generated axial algebras of Jordan type $\frac{1}{2}$

Ravil Bildanov, Ilya Gorshkov

Axial algebras of Jordan type $I^\cdot$ are a special type of commutative non-associative algebras. They are generated by idempotents whose adjoint operators have the minimal polynomial…

math.RA2024

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…

math.RA2024

Solid subalgebras in algebras of Jordan type half

I. Gorshkov, S. Shpectorov, A. Staroletov

The class of algebras of Jordan type $I^\cdot$ was introduced by Hall, Rehren and Shpectorov in 2015 within the much broader class of axial algebras. Algebras of Jordan type are commuta…

Axial Algebras: Questions and Conjectures

Groups of generalized Moufang type and Z2​-graded algebras

On 3-generated axial algebras of Jordan type 21​

Axial view on pseudo-composition algebras and train algebras of rank 3

Solid subalgebras in algebras of Jordan type half

Groups of generalized Moufang type and $Z_{2}$ -graded algebras

On $3$ -generated axial algebras of Jordan type $\frac{1}{2}$