63 citations · 63 across the 6 of their papers we have counts for
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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…
Solid subalgebras in algebras of Jordan type half
I. Gorshkov, S. Shpectorov, A. Staroletov
The class of algebras of Jordan type was introduced by Hall, Rehren and Shpectorov in 2015 within the much broader class of axial algebras. Algebras of Jordan type are commutat…
Universal Axial Algebras and a Theorem of Sakuma
J. I. Hall, F. Rehren, S. Shpectorov
In the first half of this paper, we define axial algebras: nonassociative commutative algebras generated by axes, that is, semisimple idempotents---the prototypical example of whic…