14 citations · 14 across the 7 of their papers we have counts for
11 papers
Dice periodic groups
Victor Petrogradsky
We construct a family of finitely generated infinite periodic groups. The basic example is a 2-group, called the tetrahedron group. We generalize the construction by suggesting a f…
Fibonacci Lie algebra revisited
Victor Petrogradsky
We describe old and prove new results on properties of the Fibonacci Lie algebra in a self-contained exposition. First, we study the growth of this algebra in more details. So, we…
Schreier's type formulae and two scales for growth of Lie algebras and groups
Victor Petrogradsky
Let be a free group of rank and its subgroup of finite index. Then is also a free group and the rank of is determined by Schreier's formula $m-1=(n…
Scale for codimension growth of Poisson PI-algebras
Victor Petrogradsky
A.Regev proved that the codimension growth of an associative PI-algebra is at most exponential. The author established a scale for the codimension growth of Lie PI-algebras, which…
Identities in group rings, enveloping algebras and Poisson algebras
Victor Petrogradsky
This is a short survey of works on identical relations in group rings, enveloping algebras, Poisson symmetric algebras and other related algebraic structures. First, the classical…
Nil restricted Lie algebras of oscillating intermediate growth
Victor Petrogradsky
The Grigorchuk and Gupta-Sidki groups are natural examples of self-similar finitely generated periodic groups. The author constructed their analogue in case of restricted Lie algeb…
Clover nil restricted Lie algebras of quasi-linear growth
Victor Petrogradsky
The Grigorchuk and Gupta-Sidki groups play fundamental role in modern group theory. They are natural examples of self-similar finitely generated periodic groups. The author constru…
On Jordan doubles of slow growth of Lie superalgebras
Victor Petrogradsky, Ivan Shestakov
To an arbitrary Lie superalgebra we associate its Jordan double , which is a Jordan superalgebra. This notion was introduced by the second author before. Now…
Fractal nil graded Lie, associative, Poisson, and Jordan superalgebras
Victor Petrogradsky, Ivan Shestakov
We construct a just infinite fractal 3-generated Lie superalgebra over arbitrary field, which gives rise to an associative hull , a Poisson superalgebra $\ma…
Fractal just infinite nil Lie superalgebra of finite width
Otto Augusto de Morais Costa, Victor Petrogradsky
The Grigorchuk and Gupta-Sidki groups play fundamental role in modern group theory. Their natural analogues are self-similar nil Lie -algebras. In characteristic zero, similar e…
Lie structure of truncated symmetric Poisson algebras
Ilana Zuila Monteiro Alves, Victor Petrogradsky
The paper naturally continues series of works on identical relations of group rings, enveloping algebras, and other related algebraic structures. Let be a Lie algebra over a fi…