International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. D. ch. 1.2, p. 67
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The transformation of the monomial under the matrix is given by the polynomial which is in principle non-commutative. This polynomial can be written as a sum of the monomials in the basis taking into account the eventual (anti)symmetry of and . In this way, basis element (a monomial) is transformed to To each generator of G corresponds such an action matrix M.
The action matrix changes if one considers pseudotensors. In the case of pseudotensors, the previous equation changes to The function Det(g) is just a one-dimensional representation of the group G. The determinant is either or .