Related papers: On algebraic structures of the Hochschild complex

We show that the restricted Lie algebra structure on Hochschild cohomology is invariant under stable equivalences of Morita type between self-injective algebras. Thereby we obtain a number of positive characteristic stable invariants, such…

In this article, we extend our preceding studies on higher algebraic structures of (co)homology theories defined by a left bialgebroid (U,A). For a braided commutative Yetter-Drinfel'd algebra N, explicit expressions for the canonical…

Any Batalin-Vilkovisky algebra with a homotopy trivialization of the BV-operator gives rise to a hypercommutative algebra structure at the cochain level which, in general, contains more homotopical information than the hypercommutative…

We define the appropriate homological setting to study deformation theory of complete locally convex (curved) dg-algebras based on Positselski's contraderived categories. We define the corresponding Hochschild complex controlling…

We study morphisms between commutative $BV_\infty$ algebras and show that, under suitable additional assumptions, a quasi-isomorphism of commutative $BV_\infty$ algebras induces an identification of $\frac{\infty}{2}$-variations of Hodge…

Similar to the modular vector fields in Poisson geometry, modular derivations are defined for smooth Poisson algebras with trivial canonical bundle. By twisting Poisson module with the modular derivation, the Poisson cochain complex with…

We describe the Gerstenhaber algebra structure on the Hochschild cohomology HH*$(A)$ when $A$ is a quadratic string algebra. First we compute the Hochschild cohomology groups using Barzdell's resolution and we describe generators of these…

Motivated by the recent work of Batkam-Tcheka on pointed multiplicative operads, we construct in this paper new chain complex algebras and two distinct bicomplex algebra structures on a free symmetric connected multiplicative differential…

In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure on the stable $\infty$-category…

In this paper the authors investigate the structure of the Hochschild cohomology for Frobenius kernels. The authors first establish some fundamental constructions to compute Hochschild cohomology by using spectral sequences. This enables us…

In this paper, we define a generalization of Khovanov-Lauda-Rouquier algebras which we call weighted Khovanov-Lauda-Rouquier algebras. We show that these algebras carry many of the same structures as the original Khovanov-Lauda-Rouquier…

We study the homology of free loop spaces via techniques arising from the theory of topological coHochschild homology (coTHH). Topological coHochschild homology is a topological analogue of the classical theory of coHochschild homology for…

We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation $R^{12}R^{23}=R^{23}R^{13}=R^{13}R^{12}$, called the FS-equation. Given a…

We introduce a theory of $*$-structures for bialgebroids and Hopf algebroids over a $*$-algebra, defined in such a way that the relevant category of (co)modules is a bar category. We show that if $H$ is a Hopf $*$-algebra then the action…

Let $G$ be a finite group or a compact connected Lie group and let $BG$ be its classifying space. Let $\mathcal{L}BG:=map(S^1,BG)$ be the free loop space of $BG$ i.e. the space of continuous maps from the circle $S^1$ to $BG$. The purpose…

We construct a Batalin-Vilkovisky (BV) algebra on moduli spaces of Riemann surfaces. This algebra is background independent in that it makes no reference to a state space of a conformal field theory. Conformal theories define a homomorphism…

We describe some recent development on the theory of formal Frobenius manifolds via a construction from differential Gerstenhaber-Batalin-Vilkovisk (DGBV) algebras and formulate a version of mirror symmetry conjecture: the extended…

Let $U$ be an affine log Calabi-Yau variety containing an open algebraic torus. We show that the naive counts of rational curves in $U$ uniquely determine a commutative associative algebra equipped with a compatible multilinear form. This…

Recently R. Cohen and V. Godin have proved that the homology of the free loop space of a closed oriented manifold with coefficients in a field has the structure of a Frobenius algebra without counit. In this short note we prove that when…

G-algebras, or Groebner bases algebras, were considered by Levandovsky, these algebras include very important families of algebras, like the Weyl algebras and the universal enveloping algebra of a finite dimensional Lie algebra. These…