15 citations · 36 across the 6 of their papers we have counts for
6 papers
Braided Differential Operators on Quantum Algebras
D. Gurevich, P. Pyatov, P. Saponov
We define the braided differential algebras which can be interpreted as quantization of the differential operator algebra defined on some algebraic varieties supplied with the acti…
Quantization of pencils with a gl-type Poisson center and braided geometry
D. I. Gurevich, P. A. Saponov
In the algebra Sym(gl(m)) we consider Poisson pencils generated by the linear Poisson-Lie bracket {,}_{gl(m)} and that corresponding to the so-called Reflection Equation Algebra. E…
Generic super-orbits in gl(m|n)* and their braided counterparts
D. I. Gurevich, P. A. Saponov
We introduce some braided varieties -- braided orbits -- by considering quotients of the so-called Reflection Equation Algebras associated with Hecke symmetries (i.e. special type…
Quantum line bundles on noncommutative sphere
D. Gurevich, P. Saponov
Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we introduce projective modules whic…
Hecke symmetries and characteristic relations on Reflection Equation algebras
D. I. Gurevich, P. N. Pyatov, P. A. Saponov
We discuss how properties of Hecke symmetry (i.e., Hecke type R-matrix) influence the algebraic structure of the corresponding Reflection Equation (RE) algebra. Analogues of the Ne…
Schwinger Equation as Singularly Perturbed Equation
V. E. Rochev, P. A. Saponov
A new approximation scheme for non-perturbative calculations in a quantum field theory is proposed. The scheme is based on investigation of solutions of the Schwinger equation with…