5 papers · 1 filter
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…
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…
On Jordan algebras that are factors of Matsuo algebras
Ilya Gorshkov, Andrey Mamontov, Alexey Staroletov
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 char…
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…