A quantum-trace determinantal formula for matrix commutators, and applications
Rings and Algebras
2010-03-30 v1
Abstract
In this paper, we establish a determinantal formula for 2 x 2 matrix commutators [X,Y] = XY - YX over a commutative ring, using (among other invariants) the quantum traces of X and Y. Special forms of this determinantal formula include a "trace version", and a "supertrace version". Some applications of these formulas are given to the study of value sets of binary quadratic forms, the factorization of 2 x 2 integral matrices, and the solution of certain simultaneous diophantine equations over commutative rings.
Keywords
Cite
@article{arxiv.1003.5420,
title = {A quantum-trace determinantal formula for matrix commutators, and applications},
author = {Dinesh Khurana and T. Y. Lam and Noam Shomron},
journal= {arXiv preprint arXiv:1003.5420},
year = {2010}
}
Comments
22 pages