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math.RA2023★ 1 cited
Burde's series of simple pre-Lie algebras
Vsevolod Gubarev
We describe automorphisms, derivations, and Rota -- Baxter operators on the series of simple pre-Lie algebras found by D. Burde in 1998.
math.RA2023★ 4 cited
Nonunital decompositions of the matrix algebra of order three
Vsevolod Gubarev
All decompositions of into a direct vector-space sum of two subalgebras such that none of the subalgebras contains the identity matrix are classified. Thus, the c…
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…