67 citations · 246 across the 43 of their papers we have counts for
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A simple construction of a simple nil ring
Vsevolod Gubarev
In 1999, A. Smoktunowicz solved a long-standing problem and constructed a simple nil ring. We present a substantial simplification of this construction found by Aristotle (Harmonic…
Extremal Rota-Baxter operators on matrix algebras
Vsevolod Gubarev
We classify all Rota-Baxter operators of weight on over a field of characteristic zero whose minimal polynomial has maximal degree and show that in both cases $λ=…
Failure of Ado-type theorems for preLie and postLie algebras
Vsevolod Gubarev
Over an arbitrary field of characteristic zero, we construct a two-dimensional preLie algebra and a two-dimensional postLie algebra that do not embed into the corresponding induced…
Simple double Lie algebras on the Laurent polynomial space
Vsevolod Gubarev
We construct a simple -double Lie algebra on for every nonzero . We then show that the analogous two-sided construction of weight zero is also simple. Both…
Injective Rota-Baxter operators of weight 1 on
Vsevolod Gubarev
We describe all injective Rota-Baxter operators of weight 1 on the polynomial algebra . When , the only one is . When $\mathrm{cha…
Inner post-Lie algebras and inner post-groups
V. Gubarev, Y. Li, Y. Sheng +1
In this paper, using extension theory and cohomological approach we introduce the notion of the obstruction class for an inner post-Lie algebra being induced by a Rota-Baxter opera…
Free Poisson Rota-Baxter algebra
Vsevolod Gubarev
We construct a free Poisson algebra endowed with a Rota-Baxter operator. The same construction works for a free Poisson algebra endowed with a Nijenhuis operator.