Gradings on Lie algebras, systolic growth, and cohopfian properties of nilpotent groups

zbMath1370.17015arXiv1403.5295MaRDI QIDQ2954318

Yves De Cornulier

Publication date: 12 January 2017

Full work available at URL: https://arxiv.org/abs/1403.5295

zbMATH Keywords

nilpotent groupsnilpotent Lie algebrasCarnot gradingscohopfian groupsLie algebra gradingssystolic growth

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Nilpotent groups (20F18) Discrete subgroups of Lie groups (22E40) Graded Lie (super)algebras (17B70) Nilpotent and solvable Lie groups (22E25) Asymptotic properties of groups (20F69) Solvable, nilpotent (super)algebras (17B30)

Related Items (17)

Full residual finiteness growths of nilpotent groups ⋮ On the logarithmic coarse structures of Lie groups and hyperbolic spaces ⋮ Cone‐equivalent nilpotent groups with different Dehn functions ⋮ Lie structures and chain ideal lattices ⋮ Formality and finiteness in rational homotopy theory ⋮ Taylor expansions of groups and filtered-formality ⋮ Gradings for nilpotent Lie algebras ⋮ Structure of normally and finitely non-co-Hopfian groups ⋮ Nilpotent Cantor actions ⋮ Local Lyapunov spectrum rigidity of nilmanifold automorphisms ⋮ Pro-groups and generalizations of a theorem of Bing ⋮ Flat compact Hermite-Lorentz manifolds in dimension 4 ⋮ Formality properties of finitely generated groups and Lie algebras ⋮ Isomorphisms between spaces of Lipschitz functions ⋮ Cantor dynamics of renormalizable groups ⋮ Strongly scale-invariant virtually polycyclic groups ⋮ Quantum homogeneous spaces of connected Hopf algebras

Cites Work

• Unnamed Item
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• Hopfian and co-Hopfian subsemigroups and extensions.
• Expanding maps and non-trivial self-covers on infra-nilmanifolds
• Determination of 7-dimensional indecomposable nilpotent complex Lie algebras by adjoining a derivation to 6-dimensional Lie algebras
• Scale-invariant groups.
• Arbitrarily large residual finiteness growth
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Infinitesimal computations in topology
• Limit groups as limits of free groups.
• Examples of Anosov diffeomorphisms
• Asymptotic cones of Lie groups and cone equivalences
• Graded nilpotent Lie algebras in low dimensions
• Endomorphisms of Kleinian groups.
• Théoremes de finitude en cohomologie galoisienne
• Groupes reductifs
• Systeme de poids sur une algèbre de Lie nilpotente
• Derivations of Lie algebras. III
• Systolic growth of linear groups
• Asymptotic growth and least common multiples in groups
• Croissance polynomiale et périodes des fonctions harmoniques
• Homogeneous Lie Algebras and Expanding Automorphisms
• Nilmanifolds with Anosov Automorphism
• ON CO-HOPFIAN NILPOTENT GROUPS
• Croissance des boules et des géodésiques fermées dans les nilvariétés
• Expanding maps on infra-nilmanifolds of homogeneous type
• On the commability and quasi-isometry classification of focal groups
• Some Theorems on Hopficity
• Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes

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