  Our goal in this paper is to make an attempt to find the largest Lie algebra
of vector fields on the indicatrix such that all its elements are tangent to
the holonomy group of a Finsler manifold. First, we introduce the notion of the
curvature algebra, generated by curvature vector fields, then we define the
infinitesimal holonomy algebra by the smallest Lie algebra of vector fields on
an indicatrix, containing the curvature vector fields and their horizontal
covariant derivatives with respect to the Berwald connection. At the end we
introduce the notion of the holonomy algebra of a Finsler manifold by all
conjugates of infinitesimal holonomy algebras by parallel translations with
respect to the Berwald connection. We prove that this holonomy algebra is
tangent to the holonomy group.
