Solution of the congruence problem for arbitrary hermitian and skew-hermitian matrices over polynomial rings
Rings and Algebras
2009-03-18 v1
Abstract
We equip the complex polynomial algebra C[t] with the involution which is the identity on C and sends t to -t. Answering a question raised by V.G. Kac, we show that every hermitian or skew-hermitian matrix over this algebra is congruent to the direct sum of 1 by 1 matrices and 2 by 2 matrices with zero diagonal. Morevover, we show that if two n by n hermitian or skew-hermitian matrices have the same invariant factors, then they are congruent. The complex field can be replaced by any algebraically closed field of characteristic not 2.
Keywords
Cite
@article{arxiv.math/0206104,
title = {Solution of the congruence problem for arbitrary hermitian and skew-hermitian matrices over polynomial rings},
author = {D. Z. Djokovic and F. Szechtman},
journal= {arXiv preprint arXiv:math/0206104},
year = {2009}
}
Comments
9 pages