TY - JOUR
T1 - Mal’tsev Correspondence and Bi-Interpretability
AU - Amaglobeli, M. G.
AU - Bokelavadze, T. Z.
AU - Myasnikov, A. G.
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to the Siberian Fund of Algebra and Logic 2025.
PY - 2024/11
Y1 - 2024/11
N2 - We study the famous Mal’tsev correspondence between nilpotent k-groups G and nilpotent Lie k-algebras L over a field k of characteristic zero from the model-theoretic, algebro-geometric, and algorithmic viewpoints. It is proved that, in this case, a group G and the corresponding Lie algebra L(G) are bi-interpretable by equations in each other. This gives a much more precise description of the correspondence, which implies that, in addition to the classical categorical properties, the group G and the algebra L(G) share many more algebraic, algorithmic, and model-theoretic properties.
AB - We study the famous Mal’tsev correspondence between nilpotent k-groups G and nilpotent Lie k-algebras L over a field k of characteristic zero from the model-theoretic, algebro-geometric, and algorithmic viewpoints. It is proved that, in this case, a group G and the corresponding Lie algebra L(G) are bi-interpretable by equations in each other. This gives a much more precise description of the correspondence, which implies that, in addition to the classical categorical properties, the group G and the algebra L(G) share many more algebraic, algorithmic, and model-theoretic properties.
KW - Diophantine problem
KW - Mal’tsev correspondence
KW - bi-interpretation
KW - geometric equivalence
KW - logical equivalence
KW - nilpotent Lie algebras
KW - nilpotent groups
UR - https://www.scopus.com/pages/publications/105017048107
UR - https://www.scopus.com/pages/publications/105017048107#tab=citedBy
U2 - 10.1007/s10469-025-09795-0
DO - 10.1007/s10469-025-09795-0
M3 - Article
AN - SCOPUS:105017048107
SN - 0002-5232
VL - 63
SP - 305
EP - 322
JO - Algebra and Logic
JF - Algebra and Logic
IS - 5
ER -