Nil graded self-similar algebras

DOI10.4171/GGD/112zbMath1229.17025OpenAlexW2061621717MaRDI QIDQ531924

Victor M. Petrogradsky, Ivan Pavlovic Shestakov, Efim I. Zelmanov

Publication date: 21 April 2011

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/ggd/112

zbMATH Keywords

growthinfinite-dimensional Lie algebraGelfand-Kirillov dimensionderivationLie algebra of vector fieldsself-similarGrigorchuk groupGupta-Sidki groupnil algebraRestricted Lie algebra

Mathematics Subject Classification ID

Growth rate, Gelfand-Kirillov dimension (16P90) Lie algebras of vector fields and related (super) algebras (17B66) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Structure theory for Lie algebras and superalgebras (17B05) Infinite-dimensional Lie (super)algebras (17B65) Rings of differential operators (associative algebraic aspects) (16S32) Modular Lie (super)algebras (17B50)

Related Items (14)

Some thoughts on the current state of the theory of identical relations in Lie algebras ⋮ How far can we go with Amitsur's theorem in differential polynomial rings? ⋮ Fractal nil graded Lie superalgebras ⋮ Clover nil restricted Lie algebras of quasi-linear growth ⋮ Fractal just infinite nil Lie superalgebra of finite width ⋮ On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation ⋮ Gelfand-Kirillov dimension of bicommutative algebras ⋮ A note on set-theoretic solutions of the Yang-Baxter equation ⋮ Self-similar associative algebras. ⋮ Nil restricted Lie algebras of oscillating intermediate growth ⋮ Fractal nil graded Lie, associative, Poisson, and Jordan superalgebras ⋮ On Jordan doubles of slow growth of Lie superalgebras ⋮ Nil Liep-algebras of slow growth ⋮ A retrospect of the research in nonassociative algebras in IME-USP

Cites Work

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• A sum of two locally nilpotent rings may be not nil
• On the Burnside problem for periodic groups
• On Burnside's problem on periodic groups
• Infinite dimensional Lie superalgebras
• Über die Gelfand-Kirillov-Dimension. (On the Gelfand-Kirillov-dimension)
• Branch rings, thinned rings, tree enveloping rings.
• Sur les corps liés aux algèbres enveloppantes des algèbres de Lie
• POLYCYCLIC RESTRICTED LIE ALGEBRAS
• On some types of intermediate growth in Lie algebras
• Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras
• Branch groups

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