Vladimir Dotsenko

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20242026

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math.RT2026

Young's lattice, invariant ideals, and weak identities

Vladimir Dotsenko, Artem Lopatin

For a $d$ -dimensional vector space $V$ over a field of characteristic zero, we show that $G L (V)$ -stable ideals of the universal enveloping algebra of the free two-step nilpotent Li…

math.RA2026

A Nielsen--Schreier variety of algebras without the PBW property

Vladimir Dotsenko, Bekzat Zhakhayev

We prove the Nielsen--Schreier property for the variety of algebras defined by the identity $x (x^{2})^{2} = (x^{2})^{2} x$ : every subalgebra of every free algebra in this variety is itself fr…