arXiv subjects

A. A. Davydov

Publications and source records attributed to A. A. Davydov.

5 recordsLinked to original sources

arXiv2003

Generic singularities of implicit systems of first order differential equations on the plane

For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the well known singularities of generic vector fields on the plane and the singularities described by a generic first order implicit differential equations, there exists only one generic singularity described by the implicit first order equation supplied by Whitney umbrella surface generically embedded to the space of directions on the plane.

math.DS↗

arXiv2002

Splitting of Gysin extensions

Let X --> B be an orientable sphere bundle. Its Gysin sequence exhibits H^*(X) as an extension of H^*(B)-modules. We prove that the class of this extension is the image of a canonical class that we define in the Hochschild 3-cohomology of H^*(B), corresponding to a component of its A_infty-structure, and generalizing the Massey triple product. We identify two cases where this class vanishes, so that the Gysin extension is split. The first, with rational coefficients, is that where B is a formal space; the second, with integer coefficients, is where B is a torus.

math.AT↗

arXiv1997

On some Hochschild cohomology classes of fusion algebras

The obstructions for an arbitrary fusion algebra to be a fusion algebra of some semisimple monoidal category are constructed. Those obstructions lie in groups which are closely related to the Hochschild cohomology of fusion algebras with coefficients in the K-theory of the ground (algebraically closed) field.

q-alg↗

arXiv1997

Quasitriangular structures on cocommutative Hopf algebras

The article is devoted to the describtion of quasitriangular structures (universal R-matrices) on cocommutative Hopf algebras. It is known that such structures are concentrated on finite dimensional Hopf subalgebras. In particular, quasitriangular structure on group algebra is defined by the pairs of normal inclusions of an finite abelian group and by invariant bimultiplicative form on it. The structure is triangular in the case of coinciding inclusions and skewsymmetric form. The nonstandart $λ$-structure on the representation ring of finite group, corresponding to the triangular structure on group ring, is described.

q-alg↗

arXiv1997

Twisting of monoidal structures

This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a (non-abelian) c ohomological nature. Using this fact the maps from the sets of twistings to some cohomology groups (Hochschild cohomology of K-theory) are constructed. The examples of monoidal categories of bimodules over some algebra, modules and comodules over bialgeb ra are examined. We specially concentrate on the case of free tensor category.

q-alg↗