1999/12/30 by A. P. Isaev, A. Isaev, Isaev, A. +5
Mathematics · Physics and Astronomy · #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:81R50
paper · pdf · doi:10.48550/arxiv.math/9912231
LaTeX, 12 pages. Lecture given at the 3rd International Workshop on "Lie Theory and Its Applications in Physics - Lie III", 11 - 14 July 1999, Clausthal, Germany
arxiv created 1999/12/30 · openalex publication_date 1999/12/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Cayley-Hamilton-Newton theorem - which underlies the Newton identities and the Cayley-Hamilton identity - is reviewed, first, for the classical matrices with commuting entries, second, for two q-matrix algebras, the RTT-algebra and the RLRL-algebra. The Cayley-Hamilton-Newton identities for these q-algebras are related by the factorization map. A class of algebras M(R,F) is presented. The algebras M(R,F) include the RTT-algebra and the RLRL-algebra as particular cases. The algebra M(R,F) is defined by a pair of compatible matrices R and F. The Cayley-Hamilton-Newton theorem for the algebras M(R,F) is stated. A nontrivial example of a compatible pair is given.