Related papers: Compatible actions and non-abelian tensor products

We study some properties of the non-abelian tensor product of Hom-Lie algebras concerning the preservation of products and quotients, solvability and nilpotency, and describe compatibility with the universal central extensions of perfect…

Let $G$ be a group. We denote by $\nu(G)$ an extension of the non-abelian tensor square $G \otimes G$ by $G \times G$. We prove that if $G$ is finite-by-nilpotent, then the non-abelian tensor square $G \otimes G$ is finite-by-nilpotent.…

Let $G$ and $H$ be unital associative algebras over a field $K$, such that $G$ satisfies the identity $[x_1, \dots, x_p] = 0$ for some integer $p \geq 3$ and $H$ satisfies the identities $[x_1, x_2, x_3] = 0$ and $[x_1, x_2] \cdots…

We develop a theory of crossed products by "actions" of Hecke pairs $(G, \Gamma)$, motivated by applications in non-abelian $C^*$-duality. Our approach gives back the usual crossed product construction whenever $G / \Gamma$ is a group and…

We show that the tensor product $A\otimes B$ over $\mathbb{C}$ of two $C^* $-algebras satisfying the \textit{NCDL} conditions has again the same property. We use this result to describe the $C^* $-algebra of the Heisenberg motion groups…

We define and study fibrations of topological groupoids. We interpret a groupoid fibration L->H with fibre G as an action of H on G by groupoid equivalences. Our main result shows that a crossed product for an action of L is isomorphic to…

Given a partial action \alpha of a group G on an associative algebra A we consider the crossed product A x_\alpha G. Using the algebras of multipliers of ideals of A we prove that A x_\alpha G is associative, provided that all ideals of A…

Pairings are particular bilinear maps, and as any bilinear maps they factor through the tensor product as group homomorphisms. Besides, nothing seems to prevent us to construct pairings on other abelian groups than elliptic curves or more…

We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…

We study the tensor product of an associative and a nonassociative cyclic algebra. The condition for the tensor product to be a division algebra equals the classical one for the tensor product of two associative cyclic algebras by Albert or…

Let P be a quadratic operad. We determine an associated operad ~P such that for any P-algebra A and any ~P-algebra B then the tensor product $A \otimes B$ is a P-algebra.

This paper is a new contribution to the partial Galois theory of groups. First, given a unital partial action $\alpha_G$ of a finite group $G$ on an algebra $S$ such that $S$ is an $\alpha_G$-partial Galois extension of $S^{\alpha_G}$ and a…

Let (G) be a connected compact non-abelian Lie-group and (T) a maximal torus of (G). A torus manifold with (G)-action is defined to be a smooth connected closed oriented manifold of dimension (2\dim T) with an almost effective action of (G)…

For an action $\alpha$ of a group $G$ on an algebra $R$ (over $\Bbb C$), the crossed product $R\times_\alpha G$ is the vector space of $R$-valued functions with finite support in $G$, together with the twisted convolution product given by…

We introduce the non-abelian tensor product of Lie superalgebras, study some of its properties including nilpotency, solvability and Engel, and we use it to describe the universal central extensions of Lie superalgebras. We present the…

Let G be a simple non-compact linear connected Lie group and H be a closed non-compact semisimple subgroup. We are interested in finding classes of homogeneous spaces G/H admitting proper actions of discrete non virtually abelian subgroups…

Generalizing work by Pinzari and Roberts, we characterize actions of a compact quantum group G on C*-algebras in terms of what we call weak unitary tensor functors from Rep G into categories of C*-correspondences. We discuss the relation of…

In this paper we study tensor products of affine abelian group schemes over a perfect field $k.$ We first prove that the tensor product $G_1 \otimes G_2$ of two affine abelian group schemes $G_1,G_2$ over a perfect field $k$ exists. We then…

Given two Lie $\infty$-algebras $E$ and $V$, any Lie $\infty$-action of $E$ on $V$ defines a Lie $\infty$-algebra structure on $E\oplus V$. Some compatibility between the action and the Lie $\infty$-structure on $V$ is needed to obtain a…

We prove that if $H$ is a topological group such that all closed subgroups of $H$ are separable, then the product $G\times H$ has the same property for every separable compact group $G$. Let $c$ be the cardinality of the continuum. Assuming…