Solutions of the Yang-Baxter   matrix equation for an idempotent

A. Cibotarica; Jiu Ding; J. Kolibal; Noah H. Rhee

doi:10.3934/naco.2013.3.347

Article Contents

2013, Volume 3, Issue 2: 347-352. Doi: 10.3934/naco.2013.3.347

This issue Previous Article An adaptive wavelet method and its analysis for parabolic equations Next Article Weak and strong convergence of prox-penalization and splitting algorithms for bilevel equilibrium problems

Solutions of the Yang-Baxter matrix equation for an idempotent

1.
Department of Mathematics, The Univeristy of Southern Mississippi, Hattiesburg, MS 39406-5045
2.
Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406-5045
3.
Department of Mathematics, The Univeristy of New Haven, West Haven, CT 06516
4.
Department of mathematics and Statistics, The University of Missouri - Kansas City, Kansas City, MO 64110-2499

Received: March 2012

Revised: March 2013

Published: April 2013

Abstract / Introduction Related Papers Cited by

Abstract

Let $A$ be a square matrix which is an idempotent. We find all solutions of the matrix equation of $AXA=XAX$ by using the diagonalization technique for $A$.

Keywords:

Mathematics Subject Classification: Primary: 15A18, 15A24; Secondary: 15A27.

Citation:

Related Papers

Cited by

References

[1]	R. Baxter, Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain II eqivalence to a generalized ice-type lattice model, Ann Phys., 76 (1973), 25-47.doi: 10.1016/0003-4916(73)90440-5.
[2]	A. Cibotarica, "An Examination of the Yang-Baxter Equation,'' Master thesis, University of Southern Mississippi in Hattiesberg, 2011.
[3]	J. Ding and N. Rhee, A nontrivial solution to a stochastic matrix equation, East Asia J. Applied Math., 2 (2012), 277-284.
[4]	F. Felix, "Nonlinear Equations, Quantum Groups and Duality Theorems: A Primer on the Yang-Baxter Equation," VDM Verlag, 2009.
[5]	M. Jimbo, "Introduction to the Yang-Baxter equation,'' Braid Group, Knot Theory and Statistical Physics II, World Scientific, (1994), 153-176.
[6]	C. N. Yang, Some exact results for the many-body problem in one dimension with repulsive delta function interaction, Phys. Rev. Lett., 19 (1967), 1312-1315.doi: 10.1103/PhysRevLett.19.1312.
[7]	C. N. Yang and M. L. Ge, "Braid Group, Knot Theory and Statistical Physics II,'' World Scientific, 1994.