3 papers
math.RA2026
Just-infinite Jordan Banach algebras
Victor Zhelyabin, Andrey Mamontov
By analogy with the well-established notions of just-infinite groups and just-infinite algebras, in particular -algebras, we initiate a study of just-infinite -algebras, i…
math.RA2026
Radicals in primitive axial algebras
Andrey Mamontov, Sergey Shpectorov, Victor Zhelyabin
The paper contributes to the structure theory of primitive axial algebras. For a primitive axial algebra with a Frobenius form we compare the largest ideal not containin…
math.RA2023
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…