Automorphisms of Tensor Completions of Algebras

Abstract

In the classical representation of different groups, frequent use is made of a linear automorphism group of various algebras. Since the linear automorphism group is only part of a full automorphism group, such an approach might seem to be too restrictive. In this connection, we point out a natural, wide class of algebras whose automorphisms are standard and are reducible to linear. Thus, for algebras in this class, studying the full automorphism group reduces to treating the linear, a traditional approach in the class of such algebras being quite general.

Isomorphically rigid algebras

“…Definition 3 [2]. Let L be a field, V be an indecomposable L-algebra, and K be a field extension of L in a centroid Γ L (V ), the centroid satisfying the condition that K ∩ A L (V ) = 0.…”

“…In [2], the property of being rigid for algebras under automorphisms was explored (see also [3]). Here, we look at such properties for algebras under abstract isomorphisms.…”

“…. , n, V φ i = W i ; (2) there is a field isomorphism σ : K → L such that (αx) φ ∈ α σ x φ + W i+1 for any x ∈ V i and any α ∈ K.…”