Related papers: Linearity problem for non-abelian tensor products

The purpose of this article is to study the existence of Deligne's tensor product of abelian categories by comparing it with the well-known ten- sor product of finitely cocomplete categories. The main result states that the former exists…

Let F be a finite extension of Qp and G be GL(2,F). When V is the tensor product of three admissible, irreducible, finite dimensional representations of G, the space of G-invariant linear forms has dimension at most one. When a non zero…

We explain how, in the context of a semi-abelian category, the concept of an internal crossed square may be used to set up an intrinsic approach to the Brown-Loday non-abelian tensor product.

We show that an HNN-extension with finitely generated abelian base group is Z-linear if and only if it is residually finite.

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such…

The present paper is a note on the tensor degree of finite groups, introduced recently in literature. This numerical invariant generalizes the commutativity degree through the notion of nonabelian tensor square. We show two inequalities,…

We present a novel construction of linear deformations for Lie algebras and use it to prove the non-rigidity of several classes of Lie algebras in different varieties. We consider the family of Lie algebras with an abelian factor showing…

In this paper we completely classify irreducible tensor products of covering groups of symmetric and alternating groups in characteristic $\not=2$.

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…

The consistent, local, smooth deformations of the dual formulation of linearized gravity involving a tensor field in the exotic representation of the Lorentz group with Young symmetry type (D-3,1) (one column of length D-3 and one column of…

Let $\otimes$ be the map which classifies the tensor product of two line bundles, an extension of this map to the space of all codimension 1 algebraic cycles is constructed. It is proved that this extension cannot exist in codimension…

It is known that a linear system with a system matrix A constitutes a Hamiltonian system with a quadratic Hamiltonian if and only if A is a Hamiltonian matrix. This provides a straightforward method to verify whether a linear system is…

We define graph products of families of pairs of groups and study the question when two such graph products are commensurable. As an application we prove linearity of certain graph products.

We decompose the tensor product of two irreducible representations of $\mathrm{GL}_2(\mathbb{F}_q)$ for odd $q$ and classify the pairs such that their tensor product is multiplicity free. We also classify the pairs such that their tensor…

Let A be an abelian surface over a fixed number field. If A is principally polarised, then it is known that the order of the Tate-Shafarevich group of A must, if finite, be a square or twice a square. The situation for A not principally…

We prove that if a linear group $\Gamma \subset \mathrm{GL}_n(K)$ over a field $K$ of characteristic zero is boundedly generated by semi-simple (diagonalizable) elements then it is virtually solvable. As a consequence, one obtains that…

Basis tensor gauge theory is a vierbein analog reformulation of ordinary gauge theories in which the difference of local field degrees of freedom has the interpretation of an object similar to a Wilson line. Here we present a non-Abelian…

We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.

We introduce and systematically study linear sofic groups and linear sofic algebras. This generalizes amenable and LEF groups and algebras. We prove that a group is linear sofic if and only if its group algebra is linear sofic. We show that…

Let $G$ be a dp-minimal group; we prove some consequences of several different hypotheses on $G$. First, if $G$ is torsion-free, then it is abelian. Second, if $G$ admits a distal f-generic type, then it is virtually nilpotent; we prove…