Q-multilinear Algebra

Details Q-multilinear Algebra Q-multilinear Algebra

1999-12-30

arxiv.org/abs/math/9912231v1

Mathematics

Quantum Algebra

LaTeX, 12 pages. Lecture given at the 3rd International Workshop on "Lie Theory and Its Applications in Physics - Lie III", 11

Scientific paper

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.

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