Visualization for Petrov's Odd Unitary Group
Group Theory
2021-12-16 v1
Abstract
In this article we define a set of matrices analogous to Vaserstein-type matrices which was introduced in the paper `Serre's problem on projective modules over polynomial rings and algebraic K-theory' by Suslin-Vaserstein in 1976. We prove that these are elementary linear matrices. Also, under some conditions, these matrices belong to Petrov's odd unitary group which is a generalization of all classical groups. We also prove that the group generated by these matrices is a conjugate of the Petrov's odd elementary hyperbolic unitary group when the ring is commutative.
Cite
@article{arxiv.2112.07904,
title = {Visualization for Petrov's Odd Unitary Group},
author = {A. A. Ambily and V. K. Aparna Pradeep},
journal= {arXiv preprint arXiv:2112.07904},
year = {2021}
}