Yushchenko A. V.
The forms and representations of the Lie algebra sl2(Z)
We study the structure of integral p-adic forms of the splitting
three-dimensional simple Lie algebra over the field of p-adic
numbers. We discuss the questions of diagonalizability of such forms
and description for maximal diagonal ideals. We consider torsion-free
finite-dimensional modules over the splitting three-dimensional simple
Lie algebra with integral and p-adic integral coefficients.
We describe diagonal modules, demonstrate finiteness of the number of
modules in each dimension, and prove a local-global principle for irreducible