5 papers
On primitive -generated axial algebras of Jordan type
Ilya Gorshkov, Alexey Staroletov
Axial algebras of Jordan type are commutative algebras generated by idempotents whose adjoint operators have the minimal polynomial dividing , where $η\not\in\{0,1…
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…
The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups
Nanying Yang, Alexey Staroletov
Denote the alternating and symmetric groups of degree by and respectively. Consider a permutation all of whose nontrivial cycles are of the same length.…
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…
On groups having the prime graph as alternating and symmetric groups
Ilya Gorshkov, Alexey Staroletov
The {\it prime graph} of a finite group is the graph whose vertex set is the set of prime divisors of and in which two distinct vertices and are adjacent i…