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Isomorphy Classes of Finite Order Automorphisms of SL(2, k)

In this paper, we consider the order m k-automorphisms of SL(2,k). We first characterize the forms that order m k-automorphisms of SL(2,k) take and then we simple conditions on matrices A and B, involving eigenvalues and the field that the entries of A and B lie in, that are equivalent to isomorphy between the order m k-automorphisms Inn_A and Inn_B. We examine the number of isomorphy classes and conclude with examples for selected fields.

preprint2015arXivOpen access
Robert W. BenimMark HunnellAmanda K. Sutherland
math.RT
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Robert W. BenimMark HunnellAmanda K. Sutherland

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