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On R-matrix representations of Birman-Murakami-Wenzl algebras
A. P. Isaev, O. V. Ogievetsky, P. N. Pyatov
We show that to every local representation of the Birman-Murakami-Wenzl algebra defined by a skew-invertible R-matrix one can associate pairings $V\otimes V\…
Q-multilinear Algebra
A. Isaev, O. Ogievetsky, P. Pyatov
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,…
Cayley-Hamilton-Newton identities and quasitriangular Hopf algebras
A. P. Isaev, O. V. Ogievetsky, P. N. Pyatov
In the framework of the Drinfeld theory of twists in Hopf algebras we construct quantum matrix algebras which generalize the Reflection Equation and the RTT algebras. Finite-dimens…
Modified Affine Hecke Algebras and Drinfeldians of Type A
V. N. Tolstoy, O. V. Ogievetsky, P. N. Pyatov +1
We introduce a modified affine Hecke algebra $\h{H}^{+}_{qη}({l})$ ($\h{H}_{qη}({l})$) which depends on two deformation parameters and . When the parameter is equal to z…