A quantum-trace determinantal formula for matrix commutators, and applications
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.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.