Related papers: A Diagonal on the Associahedra

OCHA is the homotopy algebra of open-closed strings. It can be defined as a sequence of multilinear operations on a pair of DG spaces satisfying certain relations which include the $L_\infty$ relations in one space and the $A_\infty$…

We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint…

In this paper, we compute the homology group and cohomology algebra of various polyhedral product objects uniformly from the point of view of diagonal tensor product. As applications, we introduce the polyhedral product method into…

Let A be an A_\infty ring spectrum. We use the description from [2] of the cyclic bar and cobar construction to give a direct definition of topological Hochschild homology and cohomology of A using the Stasheff associahedra and another…

We show that the family of chain modules over the standard simplices can be equipped with an operad structure. Similarly, the family of cochain modules of the Stasheff polytopes can be equipped with an operad structure. We first show that…

We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are "componentwise" tensor…

A dendriform algebra is an associative algebra whose product splits into two binary operations and the associativity splits into three new identities. These algebras arise naturally from some combinatorial objects and through Rota-Baxter…

Let $G$ be a group, $\mathcal{P}_G$ be the family of all subsets of $G$. For a subset $A\subseteq G$, we put $\Delta(A)=\{g\in G:|gA\cap A|=\infty\}$. The mapping $\Delta:\mathcal{P}_G\rightarrow\mathcal{P}_G$, $A\mapsto\Delta(A)$, is…

We compute the structure relations in special A_\infty-bialgebras whose operations are limited to those defining the underlying A_\infty-(co)algebra substructure. Such bialgebras appear as the homology of certain loop spaces. Whereas…

A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…

Let C be a coalgebra over a field k and A its dual algebra. The category of C-comodules is equivalent to a category of A-modules. We use this to interpret the cotensor product M \square N of two comodules in terms of the appropriate…

The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…

The symmetric homology of a unital associative algebra $A$ over a commutative ground ring $k$, denoted $HS_*(A)$, is defined using derived functors and the symmetric bar construction of Fiedorowicz. In this paper we show that $HS_*(A)$…

A coproduct on a vector space $A$ is defined as a linear map $\Delta:A\to A\otimes A$ satisfying coassociativity $(\Delta\otimes\iota)\Delta=(\iota\otimes\Delta)\Delta$. We use $\iota$ for the identity map. If $G$ is a finite group and if…

We give a new definition for the crossed-product of a C*-algebra A by a *-endomorphism \alpha, which depends not only on the pair (A,\alpha) but also on the choice of a transfer operator (defined in the paper). With this we generalize some…

Let ${\cal A}_1$ be the class of all unital separable simple $C^*$-algebras $A$ such that $A\otimes U$ has tracial rank at most one for all UHF-algebras of infinite type. It has been shown that amenable ${\cal Z}$-stable $C^*$-algebras in…

In recent years the theory of dendroidal sets has emerged as an important framework for higher algebra. In this article we introduce the concept of a $C^*$-algebraic drawing of a dendroidal set. It depicts a dendroidal set as an object in…

The notion of extension of a given $C^*$-category $C$ by a $C^*$-algebra $A$ is introduced. In the commutative case $A = C(\Omega)$, the objects of the extension category are interpreted as fiber bundles over $\Omega$ of objects belonging…

We study adjointable, bounded operators on the direct sum of two copies of the standard Hilbert C*-module over a unital C*-algebra A that are given by upper triangular 2 by 2 operator matrices. Using the definition of A-Fredholm and…

A derived operation is a bilinear operation on a commutative associative algebra $A$ defined intrinsically out of its product and several derivations of the product. We show that operators of left (or right) multiplications of a derived…