DEFINING RELATIONS OF THE SPECIAL UNITARY GROUP OVER A QUADRATIC EXTENSION OF AN ORDERED EUCLIDEAN FIELD
Zh. S. Satarov · Mathematics of the USSR-Sbornik · 1986
Let be an ordered Euclidean field (i.e., an ordered field in which the group of nonzero squares coincides with the group of positive elements) and its quadratic extension. Further, let denote the image of the element under the nontrivial automorphism of the extension . We consider the special unitary group of degree over the field , i.e., the subgroup of matrices of the general linear group for which and , where denotes taking conjugate-transpose, i.e., . Defining relations in a certain natural system of generators are found for the group , .Bibliography: 8 titles.