A quantum-trace determinantal formula for matrix commutators, and applications - Mathematics > Rings and AlgebrasReport as inadecuate




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Abstract: In this paper, we establish a determinantal formula for 2 x 2 matrixcommutators X,Y = XY - YX over a commutative ring, using among otherinvariants the quantum traces of X and Y. Special forms of this determinantalformula include a -trace version-, and a -supertrace version-. Someapplications of these formulas are given to the study of value sets of binaryquadratic forms, the factorization of 2 x 2 integral matrices, and the solutionof certain simultaneous diophantine equations over commutative rings.



Author: Dinesh Khurana, T. Y. Lam, Noam Shomron

Source: https://arxiv.org/







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