The algebraic structure of f(Q) gravity

In this paper, we focus on investigating the algebraic structure of f(Q) gravity. We introduce the basic concepts of f(Q) gravity and its Lagrangian density to do so. Using the variation principle, we derive the field equations of f(Q) gravity and show that it is a modification of the standard gravity theory, where an arbitrary function of the torsion tensor replaces the torsion scalar.We further explore the algebraic structure of f(Q) gravity and demonstrate that it can be described by a set of algebraic equations. Additionally, we delve into the symmetries of f(Q) gravity and examine their relation to the algebraic structure. This research provides valuable insights into the behavior of the theory and may lead to a better understanding of the nature of gravity and the universe's structure.