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A special decomposition (called the near standard form) of (1,2)-matrices over a ring is introduced and a method for a reduction of such matrices is explained. This can be applied for a detection of elementary second order matrices among invertible second order matrices. The tool is used in detail over orders of imaginary quadratic fields, where an algorithm, a number of properties and examples are presented.
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In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal geometry.