## Osaka Journal of Mathematics

### On the classifications of unitary matrices

#### Abstract

We classify the dynamical action of matrices in $\mathrm{SU}(p, q)$ using the coefficients of their characteristic polynomial. This generalises earlier work of Goldman for $\mathrm{SU}(2, 1)$ and the classical result for $\mathrm{SU}(1, 1)$, which is conjugate to $\mathrm{SL}(2, \mathbb{R})$. As geometrical applications, we show how this enables us to classify automorphisms of real and complex hyperbolic space and anti de Sitter space.

#### Article information

Source
Osaka J. Math., Volume 52, Number 4 (2015), 959-993.

Dates
First available in Project Euclid: 18 November 2015

https://projecteuclid.org/euclid.ojm/1447856028

Mathematical Reviews number (MathSciNet)
MR3426624

Zentralblatt MATH identifier
1336.51006

Subjects
Secondary: 20H20: Other matrix groups over fields

#### Citation

Gongopadhyay, Krishnendu; Parker, John R.; Parsad, Shiv. On the classifications of unitary matrices. Osaka J. Math. 52 (2015), no. 4, 959--993. https://projecteuclid.org/euclid.ojm/1447856028

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