13 citations · 71 across the 20 of their papers we have counts for
20 papers
Levi-Civita connection on the irreducible quantum flag manifolds
Jyotishman Bhowmick, Bappa Ghosh, Andrey O. Krutov +1
We classify covariant metrics (in the sense of Beggs and Majid) on a class of quantum homogeneous spaces. In particular, our classification implies the existence of a unique (up to…
Quantised -differential algebras
Andrey Krutov, Pavle Pandžić
We propose a definition of a quantised -differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised C…
Curvature of positive relative line modules over the quantum projective spaces
Andrey O. Krutov, Réamonn Ó Buachalla
We show that the curvature of a positive relative line module over quantum projective space is given by -integer deformation of its classical curvature. This generalises a resul…
Non-integrable distributions with simple infinite-dimensional Lie (super)algebras of symmetries
Andrey Krutov, Dimitry Leites, Irina Shchepochkina
Under usual locality assumptions, we classify all non-integrable distributions with simple infinite-dimensional Lie superalgebra of symmetries over : we single out 15 s…
Cubic Dirac operator for
Andrey Krutov, Pavle Pandžić
We construct the -deformed Clifford algebra of and study its properties. This allows us to define the -deformed noncommutative Weil algebra $\mathcal{W}_q(\…
Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2
Andrey Krutov, Alexei Lebedev, Dimitry Leites +1
As is well-known, the dimension of the space spanned by the non-degenerate invariant symmetric bilinear forms (NISes) on any simple finite-dimensional Lie algebra or Lie superalgeb…
Duflo-Serganova homology for exceptional modular Lie superalgebras with Cartan matrix
Andrey Krutov, Dimitry Leites, Jin Shang
For the exceptional finite-dimensional modular Lie superalgebras with indecomposable Cartan matrix , and their simple subquotients, we computed non-isomorphic…
Holomorphic Relative Hopf Modules over the Irreducible Quantum Flag Manifolds
Fredy Díaz García, Andrey Krutov, Réamonn Ó Buachalla +2
We construct covariant -deformed holomorphic structures for all finitely-generated relative Hopf modules over the irreducible quantum flag manifolds endowed with their Heckenber…
Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
Fredy Díaz García, Andrey Krutov, Réamonn Ó Buachalla +2
Noncommutative Kähler structures were recently introduced by the second author as a framework for studying noncommutative Kähler geometry on quantum homogeneous spaces. It was subs…
Restricted simple Lie (super)algebras in characteristic
Sofiane Bouarroudj, Andrey Krutov, Alexei Lebedev +2
We give explicit formulas proving restrictedness of the following Lie (super)algebras: known exceptional simple vectorial Lie (super)algebras in characteristic 3, deformed Lie (sup…
Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras
Sofiane Bouarroudj, Andrey Krutov, Dimitry Leites +1
We review the list of non-degenerate invariant (super)symmetric bilinear forms (briefly: NIS) on the following simple (relatives of) Lie (super)algebras: (a) with symmetrizable Car…
Computing symmetries and recursion operators of evolutionary super-systems using the SsTools environment
Arthemy V. Kiselev, Andrey O. Krutov, Thomas Wolf
At a very informal but practically convenient level, we discuss the step-by-step computation of nonlocal recursions for symmetry algebras of nonlinear coupled boson-fermion s…
On Gradings Modulo 2 of Simple Lie Algebras in Characteristic 2
Andrey Krutov, Alexei Lebedev
The ground field in the text is of characteristic 2. The classification of modulo 2 gradings of simple Lie algebras is vital for the classification of simple finite-dimensional Lie…
Nichols Algebras and Quantum Principal Bundles
Andrey Krutov, Réamonn Ó Buachalla, Karen R. Strung
We introduce a general framework for associating to a homogeneous quantum principal bundle a Yetter-Drinfeld module structure on the cotangent space of the base calculus. The holom…
Gardner's deformation of the Krasil'shchik-Kersten system
Arthemy V. Kiselev, Andrey O. Krutov
The classical problem of construction of Gardner's deformations for infinite-dimensional completely integrable systems of evolutionary partial differential equations (PDE) amounts…
Gardner's deformations as generators of new integrable systems
Arthemy V. Kiselev, Andrey O. Krutov
We re-address the problem of construction of new infinite-dimensional completely integrable systems on the basis of known ones, and we reveal a working mechanism for such transitio…
Non-Abelian Lie algebroids over jet spaces
Arthemy V. Kiselev, Andrey O. Krutov
We associate Hamiltonian homological evolutionary vector fields --which are the non-Abelian variational Lie algebroids' differentials-- with Lie algebra-valued zero-curvature repre…
On the (non)removability of spectral parameters in -graded zero-curvature representations and its applications
Arthemy V. Kiselev, Andrey O. Krutov
We generalise to the -graded set-up a practical method for inspecting the (non)removability of parameters in zero-curvature representations for partial differential e…
Gardner's deformations of the graded Korteweg-de Vries equations revisited
A. V. Kiselev, A. O. Krutov
We solve the Gardner deformation problem for the N=2 supersymmetric a=4 Korteweg-de Vries equation (P. Mathieu, 1988). We show that a known zero-curvature representation for this s…
Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
V. Hussin, A. V. Kiselev, A. O. Krutov +1
We prove that P.Mathieu's Open problem on constructing Gardner's deformation for the N=2 supersymmetric a=4-Korteweg-de Vries equation has no supersymmetry invariant solutions, whe…