arXiv subjects

Amanda K. Sutherland

Publications and source records attributed to Amanda K. Sutherland.

2 recordsLinked to original sources

arXiv2015

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.

math.RT↗

arXiv2014

Generalizations Of The Cartan And Iwasawa Decompositions For SL$_2(k)$

The Cartan and Iwasawa decompositions of real reductive Lie groups play a fundamental role in the representation theory of the groups and their corresponding symmetric spaces. These decompositions are defined by an involution with a compact fixed-point group, called a Cartan involution. For an arbitrary involution, one can consider similar decompositions. We offer a generalization of the Cartan and Iwasawa decompositions for algebraic groups defined over an arbitrary field $k$ and a general involution.

math.RT↗