Related papers: Functorial structure of units in a tensor product

For a homomorphism f: A --> B of commutative rings, let D(A,B) denote Ker[Pic(A) --> Pic(B)]. Let k be a field and assume that A is a f.g. k-algebra. We prove a number of finiteness results for D(A,B). Here are four of them. 1: Suppose B is…

We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…

In this paper, we consider the necessary and sufficient conditions for the tensor product of the fundamental representations for the restricted quantum loop algebras of type A at roots of unity to be irreducible.

If $k$ is a field, $A$ and $B$ $k$-algebras, $M$ a faithful left $A$-module, and $N$ a faithful left $B$-module, we recall the proof that the left $A\otimes_k B$-module $M\otimes_k N$ is again faithful. If $k$ is a general commutative ring,…

We prove that "unitary deformation K-theory" takes products of finitely generated groups to coproducts of algebra spectra over ku, the connective K-theory spectrum. Additionally, we give spectral sequences for computing the homotopy groups…

We define united K-theory for real C*-algebras, generalizing Bousfield's topological united K-theory. United K-theory incorporates three functors -- real K-theory, complex K-theory, and self-conjugate K-theory -- and the natural…

We give a description of the value of a finitary localizing invariant, such as algebraic $K$-theory, on the category of sheaves on a locally coherent space $X$. This in particular includes all spaces that arise as spectra of commutative…

We establish several results concerning tensor products, q-characters, and the block decomposition of the category of finite-dimensional representations of quantum affine algebras in the root of unity setting. In the generic case, a Weyl…

We prove that the map on Balmer spectra induced by a fully faithful geometric functor is a quotient map whose fibers are connected. This is an analogue of the Zariski Connectedness Theorem in algebraic geometry and it can be applied to a…

We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…

A ring is *unit-additive* if a sum of units is always either a unit or nilpotent. For example, $k[X]$ and $k[X]/(X^2)$ are unit-additive, but $\mathbb Z$ is not. We prove a wide-ranging theorem about unit-additivity in semigroup rings,…

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra, $U_q(\mathfrak{g})$ its quantum group, and $U_q(\mathfrak{k}) \subset U_q(\mathfrak{g})$ a quantum symmetric pair subalgebra determined by a Lie algebra automorphism $\theta$. We…

We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce…

Given a vector-space $~V~$ which is the tensor product of vector-spaces $A$ and $B$, we reconstruct $A$ and $B$ from the family of simple tensors $a{\otimes}b$ within $V$. In an application to quantum mechanics, one would be reconstructing…

We review some important facts about the structure of tensor products of finite dimensional representations of quantum affine algebras. This is done from the elementary standpoint of the representation theory of semisimple Lie algebras in…

This paper is concerned with the prime spectrum of a tensor product of algebras over a field. It seeks necessary and sufficient conditions for such a tensor product to have the S-property, strong S-property, and catenarity. Its main results…

This paper begins by noting that, in a 1969 paper in the Transactions, M.C.McCord introduced a construction that can be interpreted as a model for the categorical tensor product of a based space and a topological abelian group. This can be…

We show that in $K$-theory-like categories many corner embeddings into a discrete algebra of compact operators are invertible, and consequently functors on splitexact algebraic $KK$-theory are faithful if and only if they are faithful on…

Given a commutative noetherian ring $R$ and a finite acyclic quiver $Q$, we study the tensor triangulated category $\mathcal{D}(RQ)$ endowed with the vertexwise tensor product. We find a description of the internal hom functor and show that…

Fusion categories are fundamental objects in quantum algebra, but their definition is narrow in some respects. By definition a fusion category must be k-linear for some field k, and every simple object V is strongly simple, meaning that (V)…