Let [Formula: see text] be a field of characteristic zero, algebraically closed and [Formula: see text] be the unitary infinite-dimensional Grassmann [Formula: see text]-algebra. Our aim is to determine the minimal degree of an [Formula: see text]-polynomial satisfied by [Formula: see text]. Also, we find an explicit [Formula: see text]-identity of [Formula: see text].
We define a reflection in a tree as an involutive automorphism whose set of fixed points is a geodesic and prove that, for the case of a homogeneous tree of degree $4k$, the topological closure of the group generated by reflections has index $2$ in the group of automorphisms of the tree.
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