A. Mamontov

activity

20182023

collaborators

8 papers

math.RA2023

On Jordan algebras that are factors of Matsuo algebras

Ilya Gorshkov, Andrey Mamontov, Alexey Staroletov

We describe all finite connected 3-transposition groups whose Matsuo algebras have nontrivial factors that are Jordan algebras. As a corollary, we show that if F is a field of char…

math.GR2023

On 3-generated 6-transposition groups

Vsevolod A. Afanasev, Andrey Mamontov

We study $6$ -transposition groups, i.e. groups generated by a normal set of involutions $D$ , such that the order of the product of any two elements from $D$ does not exceed $6$ . We…

math.RA2022

Axial algebras of Monster type $(2 η, η)$ for $D$ diagrams. I

Andrey Mamontov, Alexey Staroletov

Axial algebras are a class of commutative algebras generated by idempotents, with adjoint action semisimple and satisfying a prescribed fusion law. Axial algebras were introduced b…

math.GR2020

Recognizing $A_{7}$ by its set of element orders

Enrico Jabara, Andrey Mamontov

Let $G$ be a periodic group, the spectrum $ω (G) \subseteq N$ of $G$ is the set of orders of elements in $G$ . In this paper we prove that the alternating group $A_{7}$ is u…

math.RA2020

Double axes and subalgebras of Monster type in Matsuo algebras

Alexey Galt, Vijay Joshi, Andrey Mamontov +2

Axial algebras are a class of commutative non-associative algebras generated by idempotents, called axes, with adjoint action semi-simple and satisfying a prescribed fusion law. Ax…

math.GR2018

On periodic groups isospectral to $A_{7}$

Andrey Mamontov

The spectrum of a periodic group $G$ is the set $ω (G)$ of its element orders. Consider a group $G$ such that $ω (G) = ω (A_{7})$ . Assume that $G$ has a subgroup $H$ isomorphic to $A_{4}$ ,…

math.GR2018

Minimal 3-generated Majorana algebras

Andrey Mamontov, Alexey Staroletov, Madeleine Whybrow

Majorana theory was introduced by A. A. Ivanov as the axiomatization of certain properties of the 2A-axes of the Griess algebra. Since its inception, Majorana theory has proved to…

math.GR2018

On knot groups acting on trees

Fedor Dudkin, Andrey Mamontov

A finitely generated group $G$ acting on a tree with infinite cyclic edge and vertex stabilizers is called a generalized Baumslag--Solitar group ( $GB S$ group). We prove that a 1-kn…

On Jordan algebras that are factors of Matsuo algebras

On 3-generated 6-transposition groups

Axial algebras of Monster type (2η,η) for D diagrams. I

Recognizing A7​ by its set of element orders

Double axes and subalgebras of Monster type in Matsuo algebras

On periodic groups isospectral to A7​

Minimal 3-generated Majorana algebras

On knot groups acting on trees

Axial algebras of Monster type $(2 η, η)$ for $D$ diagrams. I

Recognizing $A_{7}$ by its set of element orders

On periodic groups isospectral to $A_{7}$