arXiv subjects

Robert W. Benim

Publications and source records attributed to Robert W. Benim.

3 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↗

arXiv2015

Isomorphy Classes of $k$-Involutions of $\text{SO}(n, k,β)$, $n > 2$

A first characterization of the isomorphism classes of $k$-involutions for any reductive algebraic group defined over a perfect field was given in \cite{Helm2000} using $3$ invariants. In \cite{HWD04,Helm-Wu2002} a full classification of all $k$-involutions on $\text{SL}(n,k)$ for $k$ algebraically closed, the real numbers, the $p$-adic numbers or a finite field was provided. In this paper, we find analogous results to develop a detailed characterization of the $k$-involutions of $\text{SO}(n,k,β)$, where $β$ is any non-degenerate symmetric bilinear form and $k$ is any field not of characteristic $2$. We use these results to classify the isomorphy classes of $k$-involutions of $\text{SO}(n, k,β)$ for some bilinear forms and some fields $k$.

math.RT↗

arXiv2014

Isomorphy Classes of Involutions of $\text{SP}(2n, k)$, $n>2$

A first characterization of the isomorphism classes of $k$-involutions for any reductive algebraic groups defined over a perfect field was given by Helminck in 2000 using $3$ invariants. In 2004, Helminck, Wu, and Dometrius gave a full classification of all involutions on $\text{SL}(n,k)$ for $k$ algebraically closed, the real numbers, the $p$-adic numbers or a finite field was provided. In this paper, we build on these results to develop a detailed characterization of the involutions of $\text{SP}(2n, k)$. We use these results to classify the isomorphy classes of involutions of $\text{SP}(2n, k)$ where $k$ is any field not of characteristic 2.

math.RT↗