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Paper detail

A quantum-trace determinantal formula for matrix commutators, and applications

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.

preprint2010arXivOpen access
Dinesh KhuranaT. Y. LamNoam Shomron
math.RA
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Dinesh KhuranaT. Y. LamNoam Shomron

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