arXiv subjects

Vladimir Hinich

Publications and source records attributed to Vladimir Hinich.

21 records · Page 2Linked to original sources

arXiv1997

Homological algebra of homotopy algebras

We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed operad, on the category of modules over a fixed operad algebra. In Sections 2 - 6 we define the necessary structures and provide some standard comparison results. In Section 7 we define cotangent complex. In Section 8 we define a canonical structure of homotopy Lie algebra on the tangent complex.

q-alg↗

arXiv1996

Descent of Deligne groupoids

To any non-negatively graded dg Lie algebra $g$ over a field $k$ of characteristic zero we assign a functor $Σ_g: art/k \to Kan$ from the category of commutative local artinian $k$-algebras with the residue field $k$ to the category of Kan simplicial sets. There is a natural homotopy equivalence between $Σ_g$ and the Deligne groupoid corresponding to $g$. The main result of the paper claims that the functor $Σ$ commutes up to homotopy with the "total space" functors which assign a dg Lie algebra to a cosimplicial dg Lie algebra and a simplicial set to a cosimplicial simplicial set. This proves a conjecture of Schechtman which implies that if a deformation problem is described ``locally'' by a sheaf of dg Lie algebras $g$ on a topological space $X$ then the global deformation problem is described by the homotopy Lie algebra $RΓ(X,g)$.

alg-geom↗

arXiv1994

Deformation theory and Lie algebra homology

A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique quasi-isomorphism) associated with a problem.

alg-geom↗