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- Boris Kruglikov, Valentin Lychagin
- 2008

We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential operators. These multi-brackets generalize the higher JacobiMayer brackets, important in the study of evolutionary equations and the integrability problem. We also calculate Spencer δ-cohomology of… (More)

- Boris Kruglikov, Valentin Lychagin
- 2008

We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action. The corresponding differential invariants are determined via formal theory and lead to the notions of l-variants and l-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: We introduce a complex… (More)

The problem of local feedback equivalence for 1-dimensional control systems of the 1-st order is considered. The algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.

- BORIS KRUGLIKOV, VALENTIN LYCHAGIN
- 2005

For the Spencer δ-cohomologies of a symbolic system we construct a spectral sequence associated with a subspace. We calculate the sequence for the systems of Cohen-Macaulay type and obtain a reduction theorem, which facilitates computation of δ-cohomologies by reducing dimension of the system. Using this algebraic result we prove an efficient compatibility… (More)

The problem of feedback equivalence for control systems is considered. An algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.

- BORIS KRUGLIKOV, VALENTIN LYCHAGIN
- 2006

We discuss the dimensional characterization of the solutions space of a formally integrable system of partial differential equations and provide certain formulas for calculations of these dimensional quantities.

- Martin Bauer, Peter W. Michor, +5 authors Valentin Lychagin
- 2015

9:30–10:30 Local and global well-posedness of the fractional order EPDiff equation on Rd Boris Kolev Université d’Aix-Marseille I Of concern is the study of fractional order Sobolev-type metrics on the group of H∞-diffeomorphism of Rd and on its Sobolev completions Dq(Rd). It is shown that the Hs-Sobolev metric induces a strong and smooth Riemannian metric… (More)

- Vladislav V. Goldberg, Valentin V. Lychagin
- 2008

We present some old and recent results on rank problems and lineariz-ability of geodesic planar webs.

- Maks A. Akivis, Vladislav V. Goldberg, Valentin V. Lychagin
- 2003

We find d − 2 relative differential invariants for a d-web, d ≥ 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be linearizable. If one writes the above invariants in terms of web functions f(x, y) and g4(x, y), ..., gd(x, y), then necessary and sufficient conditions for the linearizabilty of a… (More)

- V. Lychagin
- 1993

We describe braidings and quantizations in monoidal categories over bialgebras and group algebras of compact Lie groups. We introduce a relative variant of a braiding and a quantization more suitable in quantum problems. To describe quantizations we introduce non-linear cohomologies and show their relations with Hochschild cohomologies and Poisson… (More)