A. P. Isaev
Joint Institute for Nuclear Research
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Featured researches published by A. P. Isaev.
Physics Letters B | 1991
M. Chaichian; A. P. Isaev; Jerzy Lukierski; Ziemowit Popowicz; P. Preŝnajder
Abstract We describe the q -deformations of the realisations of the conformal algebra depending on the conformal dimension parameter Δ . The particular role of the conformal dimensions Δ=0, 1 2 , 1 is pointed out. The q -deformed central extension terms, describing q -deformation of the Virasoro algebra, are derived. In the limit q → 1 one obtains the usual central term. The transformation properties of the q -deformed energy-momentum tensor ( Δ =2) consistent with the q -deformed central extension term are described.
Journal of Physics A | 1999
A. P. Isaev; Oleg Ogievetsky; Pavel Pyatov
The Cayley - Hamilton - Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras defined by a pair of compatible solutions of the Yang - Baxter equation. This class includes the RTT algebras as well as the reflection equation algebras.
Modern Physics Letters A | 1992
A. T. Filippov; A. P. Isaev; A. B. Kurdikov
Paragrassmann algebras with one and many paragrassmann variables are considered from the algebraic point of view without using the Green ansatz. A differential operator with respect to paragrassmann variable and a covariant para-super-derivative are introduced giving a natural generalization of the Grassmann calculus to a paragrassmann one. Deep relations between paragrassmann algebras and quantum groups with deformation parameters being root of unity are established.Paragrassmann algebras with one and many paragrassmann variables are considered from the algebraic point of view without using the Green ansatz. Operators of differentiation with respect to paragrassmann variables and a covariant para-super-derivative are introduced giving a natural generalization of the Grassmann calculus to a paragrassmann one. Deep relations between paragrassmann algebras and quantum groups with deformation parameters being roots of unity are established.
International Mathematics Research Notices | 2011
A. P. Isaev; Alexander Molev; O. V. Ogievetsky
We give a new fusion procedure for the Brauer algebra by showing that all primitive idempotents can be found by evaluating a rational function in several variables. The function takes values in the Brauer algebra and has the form of a product of R-matrix type factors. In particular, this provides a one-parameter version of the fusion procedure for the symmetric group. The R-matrices are solutions of the Yang–Baxter equation associated with the classical Lie algebras of types B, C, and D. Moreover, we construct an evaluation homomorphism from a reflection equation algebra to and show that the fusion procedure provides an equivalence between natural tensor representations of with the corresponding evaluation modules.
Nuclear Physics | 2007
A. P. Isaev; O.V. Ogievetsky
Abstract Nonpolynomial baxterized solutions of reflection equations associated with affine Hecke and affine Birman–Murakami–Wenzl algebras are found. Relations to integrable spin chain models with nontrivial boundary conditions are discussed.
Journal of Physics A | 1996
A. P. Isaev
We consider the modified (or twisted) Yang - Baxter equations for the groups and supergroups. The general solutions for these equations are presented in the case of the linear quantum (super)groups. The introduction of spectral parameters in the twisted Yang - Baxter equation and its solutions are also discussed.We consider the modified (or twisted) Yang-Baxter equations for the
Physics Letters B | 1993
A. P. Isaev; Ziemowit Popowicz
SL_{q}(N)
Czechoslovak Journal of Physics | 1998
A. P. Isaev; O. Ogievetsky; Pavel Pyatov
groups and
Letters in Mathematical Physics | 2008
A. P. Isaev; Alexander Molev; A. F. Os’kin
SL_{q}(N|M)
Journal of High Energy Physics | 2013
D. Chicherin; Sergey E. Derkachov; A. P. Isaev
supergroups. The general solutions for these equations are presented in the case of the linear quantum (super)groups. The introduction of spectral parameters in the twisted Yang-Baxter equation and its solutions are also discussed.