## A description
of derivations of the algebra of symmetric tensors

*A**. Heydari**, **N. Boroojerdian and E. Peyghan*

** Address.**

Department of Mathematics and Computer Science, Amirkabir University
of Technology (Tehran Polytechnic), Tehran, Iran

**E-mail:
**a_heydari@aut.ac.ir,
broojerd@aut.ac.ir,
e_peyghan@aut.ac.ir

Abstract.

In this paper
the symmetric differential and symmetric Lie
derivative are introduced. Using these tools derivations of the algebra of symmetric tensors are classified.
We also define
a Fr\"{o}licher-Nijenhuis bracket for vector valued
symmetric tensors.

**AMSclassification**.
53C99, 53A99, 58A99.

**Keywords**. Derivation, Fr\"{o}licher-Nijenhius bracket, symmetric differential, symmetric Lie derivative, symmetric tensor.