A power Cayley-Hamilton identity for nxn matrices over a Lie nilpotent\n ring of index k

2019/09/23 by Jenö Szigeti, Szigeti, Jeno, Szilvia Szilágyi +3
Mathematics · Engineering · #Advanced Topics in Algebra #Advanced Differential Equations and Dynamical Systems #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1909.10210

Abstract

For an nxn matrix A over a Lie nilpotent ring R of index k, we prove that an\ninvariant "power" Cayley-Hamilton identity of degree (n²)2^k-2 holds. The\nright coefficients are not uniquely determined by A, and the cosets lambda_i+D,\nwith D the double commutator ideal R[[R,R],R]R of R, appear in the so-called\nsecond right characteristic polynomial of the natural image of A in the nxn\nmatrix ring M_n(R/D) over the factor ring R/D.\n

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