49 citations · 207 across the 40 of their papers we have counts for
30 papers · 1 filter
Generalised Joyal disks, -colored -operads, and higher Deligne conjecture
Boris Shoikhet
The classical Deligne conjecture (which by now has found several different proofs) says that the Hochschild cohomological complex of a small dg category over a field has a stru…
On comparison of the Tamarkin and the twisted tensor product 2-operads
Boris Shoikhet
There are known two different constructions of contractible dg 2-operads, providing a weak 2-category structure on the following dg 2-quiver of small dg 2-categories. Its vertices…
The category , derived modifications, and deformation theory of monoidal categories
Piergiorgio Panero, Boris Shoikhet
A complex , generalising the Davydov-Yetter complex of a monoidal category, is constructed. Here are -linear (dg) monoidal categories, $F,G\…
A proof of the contractibility of the 2-operad defined via the twisted tensor product
Boris Shoikhet
In our recent papers [Sh1,2], we introduced a {\it twisted tensor product} of dg categories, and provided, in terms of it, {\it a contractible 2-operad }, acting on th…
On higher structure on the operadic deformation complexes
Boris Shoikhet
In this paper, we prove that there is a canonical homotopy -algebra structure on the shifted operadic deformation complex for any operad $\mathc…
Graded Leinster monoids and generalized Deligne conjecture for 1-monoidal abelian categories
Boris Shoikhet
In our recent paper [Sh1] a version of the "generalized Deligne conjecture" for abelian -fold monoidal categories is proven. For this result says that, given an abelian mo…
The PBW property for associative algebras as an integrability condition
Boris Shoikhet
We develop an elementary method for proving the PBW theorem for associative algebras with an ascending filtration. The idea is roughly the following. At first, we deduce a proof of…
An algebra structure on polyvector fields
Boris Shoikhet
It is well-known that the Kontsevich formality [K97] for Hochschild cochains of the polynomial algebra fails if the vector space is infinite-dimensional. In the pres…
Koszul duality in deformation quantization and Tamarkin's approach to Kontsevich formality
Boris Shoikhet
Let be a quadratic Poisson bivector on a vector space . Then one can also consider as a quadratic Poisson bivector on the vector space . Fixed a universal deform…
Koszul duality in deformation quantization, I
Boris Shoikhet
Let be a polynomial Poisson bivector on a finite-dimensional vector space over . Then Kontsevich [K97] gives a formula for a quantization of the alge…
On and on a -action on the consecutive commutators of free associative algebra
Boris Feigin, Boris Shoikhet
We consider the lower central filtration of the free associative algebra with generators as a Lie algebra. We consider the associated graded Lie algebra. It is shown that…
An explicit formula for the deformation quantization of Lie bialgebras
Boris Shoikhet
A model of 3-dimensional topological quantum field theory is rigorously constructed. The results are applied to an explicit formula for deformation quantization of any finite-dimen…
Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics
Boris Feigin, Andrey Losev, Boris Shoikhet
In the present paper we discuss an independent on the Grothendieck-Sato isomorphism approach to the Riemann-Roch-Hirzebruch formula for an arbitrary differential operator. Instead…
A concept of PROP and deformation theory of (co)associative bialgebras
Boris Shoikhet
We introduce a concept of PROP generalizing the Kontsevich concept of PROP. We prove that some Stasheff-type compactification of the Kontsevich spaces de…
An explicit deformation theory of (co)associative bialgebras
Boris Shoikhet
The paper has been withdrawn.
Hochschild cohomology of the Weyl algebra and traces in deformation quantization
Boris Feigin, Giovanni Felder, Boris Shoikhet
We give a formula for a cocycle generating the Hochschild cohomology of the Weyl algebra with coefficients in its dual.It is given by an integral over the configuration space of or…
The CROCs, non-commutative deformations, and (co)associative bialgebras
Boris Shoikhet
We compactify the spaces introduced by Maxim Kontsevich. The initial idea was to construct an algebra governing the deformations of a (co)associative bialgebra.…
Tsygan formality and Duflo formula
Boris Shoikhet
We prove the 0-(co)homology part of the conjecture on the cup-products on tangent cohomology in the Tsygan formality [Sh2]. We discuss its applications to the Duflo formula.
A proof of the Tsygan formality conjecture for chains
Boris Shoikhet
We extend the Kontsevich formality -morphism $\U\colon T^\ndot_\poly(\R^d)\to\D^\ndot_\poly(\R^d)$ to an -morphism of an -modules over $T^\ndot_\poly(…
Vanishing of the Kontsevich integrals of the wheels
Boris Shoikhet
We prove that the Kontsevich integrals (in the sense of the formality theorem) of all even wheels are equal to zero. We deduce this theorem from the result of \cite{FSh} on the def…
Deformation quantization with traces and vanishing of the wheels
Boris Feigin, Boris Shoikhet
The paper has been withdrawn because the result of math.QA/0002057 "Deformation quantization with traces" holds only for a constant volume form.
Deformation quantization with traces
Giovanni Felder, Boris Shoikhet
In the present paper we prove a statement closely related to the cyclic formality conjecture. In particular, we prove that for a divergence-free Poisson bivector field on R^d, the…
Gerstenhaber bracket on double Hochschild complex and deformation theory
Boris Shoikhet
We construct a differential and a Lie bracket on the space\linebreak $\{\Hom (A^{\otimes k}, A^{\otimes l})\},_{k,l\ge 0}$ for any associative algebra . The restriction of this…
On the cyclic Formality conjecture
Boris Shoikhet
We conjecture an explicit formula for a cyclic analog of the Formality -morphism [K]. We prove that its first Taylor component, the cyclic Hochschild-Kostant-Rosenberg…