2010/03/29 by Dinesh Khurana, T. Y. Lam, Khurana, Dinesh +3
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.1003.5420
22 pages
arxiv created 2010/03/29 · openalex publication_date 2010/03/29 · arxiv updated 2010/03/30 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
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.