2 citations · 2 across the 3 of their papers we have counts for
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Splitting partially commutative Lie algebras into direct sums
Evgeny Poroshenko
In this work, we prove that partially commutative, partially commutative metabelian, or partially commutative nilpotent Lie algebra splits into the direct sum of two subalgebras if…
On Universal Equivalence of Partially Commutative Metabelian Lie Algebras
Evgeny Poroshenko
In this paper, we consider partially commutative metabelian Lie algebras whose defining graphs are cycles. We show that such algebras are universally equivalent iff the correspondi…
Centralizers in partially commutative Lie algebras (in Russian)
Evgeny Poroshenko
In this paper, the complete description of centralizers of elements in partially commutative Lie algebras is obtained. The description is given explicitly in the terms of generator…
Universal equivalence of partially commutative metabelian Lie algebras
Evgeny Poroshenko, Evgeny Timoshenko
In this paper, we find a criterium for universal equivalence of partially commutative Lie algebras whose defining graphs are trees. Besides, we obtain bases for partially commutati…
Bases for partially commutative Lie algebras
Evgeny Poroshenko
In this paper, linear bases for the partially commutative Lie algebras are found. The method of the Gröbner--Shirshov bases is used. It easily follows from the structure that the e…