Related papers: Quasi-commutative cochains in algebraic topology

We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors. Inspired by the classical theory of…

Let $\k$ be a commutative ring, and let $(A,\mfrak{a})$ be an adic ring which is a $\k$-algebra. We study complete and torsion versions of the derived Hochschild homology and cohomology functors of $A$ over $\k$. To do this, we first…

We define the secondary Hochschild complex for an entwining structure over a commutative $k$-algebra $B$. We show that this complex carries the structure of a weak comp algebra. We obtain two distinct cup product structures for the…

Let G be a general (not necessarily finite dimensional compact) Lie group, let g be its Lie algebra, let Cg be the cone on g in the category of differential graded Lie algebras, and consider the functor which assigns to a chain complex V…

We consider a class of quasi-Hopf algebras which we call \emph{generalized twisted quantum doubles}. They are abelian extensions $H = \mb{C}[\bar{G}] \bowtie \mb{C}[G]$ ($G$ is a finite group and $\bar{G}$ a homomorphic image), possibly…

In an application of the notion of twisting structures introduced by Hess and Lack, we define twisted composition products of symmetric sequences of chain complexes that are degreewise projective and finitely generated. Let Q be a cooperad…

We construct a many-object dual version of Chen's iterated integral map. For any topological space X, the construction takes the form of an A-infinity functor between two dg categories whose objects are the points of X: the domain has as…

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…

Differential graded (DG) algebras are powerful tools from rational homotopy theory. We survey some recent applications of these in the realm of homological commutative algebra.

Let X be a projective complex 3-fold, quasihomogeneous with respect to an action of a linear algebraic group. We show that X is a compactification of SL_2/G, G a discrete subgroup, or that X can be equivariantly transformed into the 3-dim.…

Let H be a Hopf algebra, A a left H-module algebra and V a left H-module A-bimodule. We study the behavior of the right A-linear endomorphisms of V under twist deformation. We in particular construct a bijective quantization map to the…

Let X=G/K be a connected Riemannian homogeneous space of a real Lie group G. The homogeneous space X is called commutative if the algebra of G-invariant differential operators on X is commutative. We prove an effective commutativity…

We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is…

In this paper we introduce the notion of Poincar\'e DGCAs of Hodge type, which is a subclass of Poincar\'e DGCAs encompassing the de Rham algebras of closed orientable manifolds. Then we introduce the notion of the small algebra and the…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

We introduce a new topological coproduct $\Delta^{\psi}_{u}$ for quantum toroidal algebras $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in all untwisted types, leading to a well-defined tensor product on the category…

This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an algebraically closed field of characteristic…

Let $K$ be an infinite field and $K< X> =K< X_1,...,X_n>$ the free associative algebra generated by $X=\{X_1,...,X_n\}$ over $K$. It is proved that if $I$ is a two-sided ideal of $K< X>$ such that the $K$-algebra $A=K< X> /I$ is almost…

We give a systematic construction of semiorthogonal decompositions of derived categories of coherent sheaves on quasi-smooth derived algebraic stacks over $\mathbb{C}$, where the summands are subcategories defined by weight conditions, and…

Injective resolutions of modules are key objects of homological algebra, which are used for the computation of derived functors. Semiinjective resolutions of chain complexes are more general objects, which are used for the computation of…