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pro vyhledávání: '"Mamontov, Andrey"'
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 decompositions of idempotents in these classes of algebras. The corresponding
Externí odkaz:
http://arxiv.org/abs/2309.05237
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 characteristic 0, then there exist infinitely many primitive axial algebra
Externí odkaz:
http://arxiv.org/abs/2305.10958
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 classify most of the groups generated by $3$ elements from $D$, two o
Externí odkaz:
http://arxiv.org/abs/2303.14144
Autor:
Mamontov, Andrey, Staroletov, Alexey
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 by Hall, Rehren, and Shpectorov in 2015 as a broad generalization of Ma
Externí odkaz:
http://arxiv.org/abs/2212.14608
Autor:
Jabara, Enrico, Mamontov, Andrey
Let $G$ be a periodic group, the spectrum $\omega(G) \subseteq \mathbb{N}$ of $G$ is the set of orders of elements in $G$. In this paper we prove that the alternating group $A_{7}$ is uniquely defined by its spectrum in the class of all groups.
Externí odkaz:
http://arxiv.org/abs/2008.06307
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. Axial algebras were introduced by Hall, Rehren and Shpectorov \cite{hrs,
Externí odkaz:
http://arxiv.org/abs/2004.11180
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Autor:
Mamontov, Andrey
The spectrum of a periodic group $G$ is the set $\omega(G)$ of its element orders. Consider a group $G$ such that $\omega(G)=\omega(A_7)$. Assume that $G$ has a subgroup $H$ isomorphic to $A_4$, whose involutions are squares of elements of order $4$.
Externí odkaz:
http://arxiv.org/abs/1810.13167
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 be a remarkable tool with which to study objects related to the Griess
Externí odkaz:
http://arxiv.org/abs/1809.03184
Autor:
Dudkin, Fedor, Mamontov, Andrey
A finitely generated group $G$ acting on a tree with infinite cyclic edge and vertex stabilizers is called a generalized Baumslag--Solitar group ($GBS$ group). We prove that a 1-knot group $G$ is $GBS$ group iff $G$ is a torus-knot group and describe
Externí odkaz:
http://arxiv.org/abs/1807.06275