Related papers: $\mathbb{Z}_3\times \mathbb{Z}_3$ crossed products

In the present article we investigate the possibility of combining the usual Grassmann algebras with their ternary Z_3-graded counterpart, thus creating a more general algebra with coexisting quadratic and cubic constitutive relations. We…

We show that if $(A,G,\alpha)$ is a groupoid dynamical system with $A$ continuous trace, then the crossed product $A\rtimes_{\alpha}G$ is Morita equivalent to the C*-algebra $C*(\underline G,\underline E)$ of a twist $\underline E$ over a…

For each valued quiver $Q$ of Dynkin type, we construct a valued ice quiver $\Delta_Q^2$. Let $G$ be a simple connected Lie group with Dynkin diagram the underlying valued graph of $Q$. The upper cluster algebra of $\Delta_Q^2$ is graded by…

Given a w*-closed unital algebra $A$ acting on $H_0$ and a contractive w*-continuous endomorphism $\beta$ of $A$, there is a w*-closed (non-selfadjoint) unital algebra $\mathbb{Z}_+\bar{\times}_\beta A$ acting on…

We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$.…

We prove that the stack-number of the strong product of three $n$-vertex paths is $\Theta(n^{1/3})$. The best previously known upper bound was $O(n)$. No non-trivial lower bound was known. This is the first explicit example of a graph…

Let $A$ be a simple, exact, separable, unital $C^*$-algebra and let $\alpha \colon G \rightarrow Aut(A)$ be an action of a finite group $G$ with the weak tracial Rokhlin property. We show that every trace on $A \rtimes_{\alpha} G$ is…

We use computer algebra to determine all the multilinear polynomial identities of degree $\le 7$ satisfied by the trilinear operations $(a \cdot b) \cdot c$ and $a \cdot (b \cdot c)$ in the free dendriform dialgebra, where $a \cdot b$ is…

Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: ``tensor product'' and ``multiplicity'' varieties. These varieties are closely related to Nakajima's…

The theorem of the title is deduced from the equivalence between crossed complexes and cubical $\omega$-groupoids with connections proved by the authors in 1981. In fact we prove the equivalence of five categories defined internally to an…

Larsen has recently extended Exel's construction of crossed products from single endomorphisms to abelian semigroups of endomorphisms, and here we study two families of her crossed products. First, we look at the natural action of the…

An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to…

Let $(\mathcal G, \Sigma)$ be an ordered abelian group with Haar measure $\mu$, let $(\mathcal A, \mathcal G, \alpha)$ be a dynamical system and let $\mathcal A\rtimes_{\alpha} \Sigma $ be the associated semicrossed product. Using Takai…

In this paper, we will prove that if $A$ is a $C^*$-algebra with an effective coaction $\epsilon$ by a compact quantum group, then the fixed point algebra and the reduced crossed product are Morita equivalent. As an application, we prove an…

We address the problem of determining the class of self-similar groups, and in particular its closure under restricted direct products. We show that the group $\mathbb Z^{(\omega)}$ is self-similar, that $G^{(\omega)}\rtimes C_2$ is…

We consider independent anisotropic bond percolation on $\mathbb{Z}^d\times \mathbb{Z}^s$ where edges parallel to $\mathbb{Z}^d$ are open with probability $p<p_c(\mathbb{Z}^d)$ and edges parallel to $\mathbb{Z}^s$ are open with probability…

Suppose that $\mathcal M$ is a countably decomposable type II$_1$ von Neumann algebra and $\mathcal A$ is a separable, non-nuclear, unital C$^*$-algebra. We show that, if $\mathcal M$ has Property $\Gamma$, then the similarity degree of…

Touchard-Riordan-like formulas are some expressions appearing in enumeration problems and as moments of orthogonal polynomials. We begin this article with a new combinatorial approach to prove these kind of formulas, related with integer…

The $\mathit{SU}(3)$ tensor multiplicities are piecewise polynomial of degree $1$ in their labels. The pieces are the chambers of a complex of cones. We describe in detail this chamber complex and determine the group of all linear…

We consider Exel's new construction of a crossed product of a C*-algebra A by an endomorphism \alpha. We prove that this crossed product is universal for an appropriate family of covariant representations, and we show that it can be…