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math.RA2025★ 1 cited
Rota-Baxter operators on the simple Jordan algebra of matrices of order two
Vsevolod Gubarev, Alexander Panasenko
We describe all Rota-Baxter operators of any weight on the space of matrices from considered under the product and usually denoted as $M_2(F)^{(+)…
math.RA2023
Generalized sharped cubic form and split spin factor algebra
Vsevolod Gubarev, Farukh Mashurov, Alexander Panasenko
There is a well-known construction of a Jordan algebra via a sharped cubic form. We introduce a generalized sharped cubic form and prove that the split spin factor algebra is induc…
math.RA2022★ 2 cited
On radicals of Novikov algebras
A. S. Panasenko
We show that in a prime nonassociative Novikov algebra every nonzero ideal is non-associative. We prove that Baer (and Andrunakievich) radical and left quasiregular radical coincid…