4 papers · 1 filter
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…
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…
Full automorphism groups of the axial algebra for and related algebras
Tendai M. Mudziiri Shumba, Sergey Shpectorov
In this paper, in continuation of arXiv:2311.18538, we compute the full automorphism groups of the 286-dimensional algebra for , its subalgebras and other related algebras.…
Radicals in flip subalgebras
Bernardo G. Rodrigues, Sergey Shpectorov
We develop methods for determining key properties (simplicity and the dimension of radical) of flip subalgebras in Matsuo algebras. These are interesting classes of commutative non…