  The paper is devoted to an algebraic analogue of a geometric approach to the
classical notion of complex dilatation suggested in the paper arXiv:1701.06259
[math.CV] by the author. At the same time it provides an invariant version of
this geometric approach.
  From the algebraic point of view it is only natural to work with a general
field extension K/k of degree 2 instead of the fields of real and complex
number (under the assumption that the characteristic is not equal to 2). Given
a k-linear map between two K-vector spaces of dimension 1 over K, there are two
natural measures of deviation of this map from being K-linear: its conformal
dilatation, defined in terms of quadratic forms over k, and its Beltrami form,
directly generalizing the classical complex dilatation. It turns out that these
two measures are related in the same way as in the classical case. Working with
a general field extension does not lead to any new difficulties compared to the
classical case, but only clarifies the algebraic aspects of the theory.
