Chair of Higher Geometry,

Department of Mathematics and Mechanics,

Saint-Petersburg State University,

28 Universitetsky Av.,

198504 Saint-Petersburg, RUSSIA

E-mail: skalnitsky@hotmail.com

**Spray algebra**

**Abstract:**

The infinite dimensional tensor algebra of polylinear symmetries of
spray of affine connection is described. Components of this graded algebra
correspond different geometrical aspects of symmetry. We are studying the
structure of the algebra, describing "standard" solutions of natural differential
operators appeared and introduce the notion of "Bochner type" obstacles
for symmetry.