7 papers
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…