Andrey Mudrov

R-matrix and Mickelsson algebras for orthosymplectic quantum groups

Journal of Mathematical Physics, 2015

Let g be a complex orthogonal or symplectic Lie algebra and g ′ ⊂ g the Lie subalgebra of rank rk... more

Quantum groupoids and dynamical categories

In this paper we realize the dynamical categories introduced in our previous paper as categories ... more In this paper we realize the dynamical categories introduced in our previous paper as categories of modules over bialgebroids; we study the bialgebroids arising in this way. We define quasitriangular structure on bialgebroids and present examples of quasitriangular bialgebroids related to the dynamical categories. We show that dynamical twists over an arbitrary base give rise to bialgebroid twists.

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The role of the quantum universal enveloping algebras of symmetries in constructing non-commutati... more The role of the quantum universal enveloping algebras of symmetries in constructing non-commutative geometry of the space-time including vector bundles, measure, equations of motion and their solutions is discussed. In the framework of the twist theory the Klein-Gordon-Fock and Dirac equations on the quantum Minkowski space are studied from this point of view for the simplest quantum deformation of the Lorentz algebra induced by its Cartan subalgebra twist.

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Inhomogeneous quantum Lie algebras

We study quantization of a class of inhomogeneous Lie bialgebras which are crossproducts in dual ... more We study quantization of a class of inhomogeneous Lie bialgebras which are crossproducts in dual sectors with Abelian invariant parts. This class forms a category stable under dualization and the double operations. The quantization turns out to be a functor commuting with them. The Hopf operations and the universal R-matrices are given in terms of generators. The quantum algebras obtained appear to be isomorphic to the universal enveloping Poisson-Lie algebras on the dual groups. 1999 1 Partially supported by the RFFI grant 98-01-00310.

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U/sub{q}(sl(n))-covariant quantization of symmetric coadjoint orbits via reflection equation algebra

ABSTRACT

Representations of quantum conjugacy classes of orthosymplectic groups

Let G be the complex symplectic or special orthogonal group and g its Lie algebra.

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New approach to summation of field-theoretical series in models with strong coupling

A new approach to summation of divergent field-theoretical series is suggested. It is based on th... more A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the knowledge of the exact asymptotic parameters. The method is tested on functions expanded in their asymptotic power series and applied to estimating the ground state energy of simple quantum mechanical problems including anisotropic oscillators and caclulating the critical exponents for certain comformal field models. It can be expected that the new approach to summation may be used to obtaining numerical estimates for important physical quantities represented by divergent series in two- and three-dimensional field models.

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Summation of divergent field-theoretical series in phase transition models with strong coupling

$Research paper thumbnail of Critical thermodynamics of three-dimensional MN-component field model with cubic anisotropy from higher-loop [iopmath latex="$\varepsilon$"] [/iopmath] expansion$

Critical thermodynamics of three-dimensional MN-component field model with cubic anisotropy from higher-loop [iopmath latex="$\varepsilon$"] [/iopmath] expansion

Journal of Physics A General Physics

The critical thermodynamics of an MN-component field model with cubic anisotropy relevant to the ... more The critical thermodynamics of an MN-component field model with cubic anisotropy relevant to the phase transitions in certain crystals with complicated ordering is studied within the four-loop [iopmath latex="$\varepsilon$"] [/iopmath] expansion using the minimal subtraction scheme. Investigation of the global structure of RG flows for the physically significant cases [iopmath latex="$M=2$"] M = 2 [/iopmath] , [iopmath latex="$N=2$"] N = 2 [/iopmath] and [iopmath latex="$M=2$"] M = 2 [/iopmath] , [iopmath latex="$N=3$"] N = 3 [/iopmath] shows that the model has an anisotropic stable fixed point with new critical exponents. The critical dimensionality of the order parameter is proved to be equal to [iopmath latex="$N_{\rm c}^{\rm C}=1.445(20)$"] NcC = 1.445(20) [/iopmath] , that is exactly half its counterpart in the real hypercubic model.

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Modified Borel summation of divergent series and critical-exponent estimates for an N-vector cubic model in three dimensions from five-loop ε expansions

Physical Review E, 1998

A new approach to summation of divergent field-theoretical series is suggested. It is based on th... more A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the exact asymptotic parameters to be known. The method is tested on functions expanded in their asymptotic power series. It is applied to estimating the critical exponent values for an N -vector field model, describing magnetic and structural phase transitions in cubic and tetragonal crystals, from five-loop ǫ expansions.

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Three-loop renormalization-group analysis of a complex model with stable fixed point: Critical exponents up to ε3 and ε4

Physical Review B, 1998

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Stability of the three-dimensional fixed point in a model with three coupling constants from the ε expansion: Three-loop results

Physical Review B, 1998

On stability of the three-dimensional fixed point in a model with three coupling constants from t... more

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Critical behavior of certain antiferromagnets with complicated ordering: Four-loop ɛ-expansion analysis

Physical Review B, 2001

The critical behavior of a complex N -component order parameter Ginzburg-Landau model with isotro... more The critical behavior of a complex N -component order parameter Ginzburg-Landau model with isotropic and cubic interactions describing antiferromagnetic and structural phase transitions in certain crystals with complicated ordering is studied in the framework of the four-loop renormalization group (RG) approach in (4 − ε) dimensions. By using dimensional regularization and the minimal subtraction scheme, the perturbative expansions for RG functions are deduced and resummed by the Borel-Leroy transformation combined with a conformal mapping. Investigation of the global structure of RG flows for the physically significant cases N = 2 and N = 3 shows that the model has an anisotropic stable fixed point governing the continuous phase transitions with new critical exponents. This is supported by the estimate of the critical dimensionality N c = 1.445(20) obtained from six loops via the exact relation N c = 1 2 n c established for the complex and real hypercubic models.

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On a Universal Solution to the Reflection Equation

For a given quasitriangular Hopf algebra H we study relations between the braided groupH * and Dr... more

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On twisting solutions to the Yang-Baxter equation

Sufficient conditions for an invertible two-tensor F to relate two solutions to the Yang-Baxter e... more

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Quantum coadjoint orbits in gl( n )*

We present a double /Ah (gl(n, C))-equivaxiant quantization on semisimple coadjoint orbits of the... more We present a double /Ah (gl(n, C))-equivaxiant quantization on semisimple coadjoint orbits of the group GL(n, C) as a quotient of the extended reflection equation algebra by relations which are given explicitly. Such a quantization is a two-parameter family including an explicit GL(n)-equivariant quantization of the Kirillov-Kostant-Souriau Poisson bracket.

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Reflection equation- and FRT-type algebras

ABSTRACT

Universal R-Matrix for Esoteric Quantum Groups

The universal R-matrix for a class of esoteric (non-standard) quantum groups U q (gl(2N + 1)) is ... more The universal R-matrix for a class of esoteric (non-standard) quantum groups U q (gl(2N + 1)) is constructed as a twisting of the universal R-matrix R S of the Drinfeld-Jimbo quantum algebras. The main part of the twisting element F is chosen to be the canonical element of appropriate pair of separated Hopf subalgebras (quantized Borel's B(N ) ⊂ U q (gl(2N + 1))), providing the factorization property of F. As a result, the esoteric quantum group generators can be expressed in terms of the Drinfeld-Jimbo ones.

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Quantization of borderline Levi conjugacy classes of orthogonal groups

Journal of Mathematical Physics, 2014

We construct equivariant quantization of a special family of Levi conjugacy classes of the comple... more

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Critical exponents for the model with unique stable fixed point from three-loop RG expansions

International Journal of Modern Physics B, 1998

The critical behavior of a model describing phase transitions in cubic and tetragonal anti-ferrom... more The critical behavior of a model describing phase transitions in cubic and tetragonal anti-ferromagnets with 2N-component (N&gt;1) real order parameters as well as the structural transition in NbO2 crystal is studied within the field-theoretical renormalization-group (RG) approach in three and (4-ε)-dimensions. Perturbative expansions for RG functions are calculated up to three-loop order and resummed, in 3D, by means of the

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