6 citations · 6 across the 8 of their papers we have counts for
9 papers
Characteristic classes on a noncommutative background: a new approach
Dimitry Gurevich, Vladimir Roubtsov, Pavel Saponov
We introduce analogues of partial derivatives with respect to the generators of the enveloping algebras U(gl(N)) and their q-deformations, the so-called modified reflection equatio…
Representations of Spectrum of GL(m) type Quantum Matrices
Dimitry Gurevich, Pavel Saponov, Mikhail Zaitsev
In the present paper we are dealing with reflection equation algebras corresponding to even skew-invertible Hecke symmetries. Our main result consists in computing th…
Braided Gelfand-Zetlin algebras and their semiclassical counterparts
Dimitry Gurevich, Pavel Saponov
We construct analogs of the Gelfand-Zetlin algebras in the Reflection Equation algebras, corresponding to Hecke symmetries, mainly to those coming from the quantum groups U_q(sl(N)…
Generalized Harish-Chandra morphism on Reflection Equation algebras
Dimitry Gurevich, Pavel Saponov
We consider the so-called generalized Harish-Chandra morphism, taking the center of the enveloping algebra U(gl(N)) to the commutative algebra generated by eigenvalues of the gener…
Yang-Mills models on Noncommutative background
Dimitry Gurevich, Pavel Saponov
In our previous publications we have developed some elements of Noncommutative calculus on the enveloping algebras of type, in particular, analogs of the partial derivatives…
Quantum Schur-Weyl duality and q-Frobenius formula related to Reflection Equation algebras
Dimitry Gurevich, Pavel Saponov
We establish a q-version of the Schur-Weyl duality, in which the role of the symmetric group is played by the Hecke algebra and the role of the enveloping algebra U(gl(N)) is playe…
Quantum vector fields via quantum doubles and their applications
Dimitry Gurevich, Pavel Saponov
By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the s…
Noncommutative geometry on central extension of U(u(2))
Dimitri Gurevich, Pavel Saponov
In our previous publications we have introduced analogs of partial derivatives on the algebras U(gl(N)). In the present paper we compare two methods of introducing these analogs: v…
Traces in braided categories
D. Gurevich, R. Leclercq, P. Saponov
With any even Hecke symmetry R (that is a Hecke type solution of the Yang-Baxter equation) we associate a quasitensor category. We formulate a condition on R implying that the cons…