TY - JOUR
T1 - Arithmetic Deformation Theory of Lie Algebras
TT -
JF - IJMSI
JO - IJMSI
VL - 18
IS - 1
UR - http://ijmsi.ir/article-1-1237-en.html
Y1 - 2023
SP - 19
EP - 32
KW - Arithemtic Lie algebras
KW - Deforfation of Lie algebras
KW - Schlessinger criteria.
N2 - This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations. In the second part, we use a version of Schlessinger criteria for functors on the Artinian category of nilpotent Lie algebras which is formulated by Pridham, and explore arithmetic deformations using this technique.
M3 10.52547/ijmsi.18.1.19
ER -