Back to Search
Start Over
A quantum-trace determinantal formula for matrix commutators, and applications
- Publication Year :
- 2010
-
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.<br />Comment: 22 pages
- Subjects :
- Mathematics - Rings and Algebras
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1003.5420
- Document Type :
- Working Paper