Related papers: Tensor products of valued fields

This paper tackles a problem on the possible transfer of regularity to tensor products of algebras over a field k. The main result establishes necessary and sufficient conditions for a Noetherian tensor product of two extension fields of k…

We prove that any tensor product factorization with a commutative factor of a modular group algebra over a prime field comes from a direct product decomposition of the group basis. This extends previous work by Carlson and Kov\'acs for the…

In this document we prove: Let $\mathbb K=(K,+,\cdot,v,\Gamma)$ be an algebraically closed valued field and let $(G,\oplus)$ be a $\mathbb K$-definable group that is either the multiplicative group or contains a finite index subgroup that…

Assume that $(L,v)$ is a finite Galois extension of a valued field $(K,v)$. We give an explicit construction of the valuation ring $\mathcal O_L$ of $L$ as an $\mathcal O_K$-algebra, and an explicit description of the module of relative…

We prove Zilber's trichotomy for reducts of ACVF expanding $(K,+)$ or $(K^*, \cdot)$.

Let (K, v) be a henselian valued field of arbitrary rank. In this paper, we give an irreducibility criterion for multivariate polynomials over K using valuation theory.

A semisimple algebraic tensor category over an algebraically closed field k of characteristic zero is the representation category of all finite dimensional twisted super representations of an affine reductive supergroup G over k. Such a…

A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…

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…

Let R\_{0,n} be the Clifford algebra of the antieuclidean vector space of dimension n. The aim is to built a function theory analogous to the one in the C case. In the latter case, the product of two holomorphic functions is holomorphic,…

The main goal of this paper is to study the structure of the graded algebra associated to a valuation. More specifically, we prove that the associated graded algebra ${\rm gr}_v(R)$ of a subring $(R,\mathfrak{m})$ of a valuation ring…

This article is a natural construction of our previous works. In this article, we employ similar ideas due to MacLane to provide an estimate of IC(K(X)|K,v) when (K(X)|K,v) is a valuation algebraic extension. Our central result is an…

We investigate the computability-theoretic properties of valued fields, and in particular algebraically closed valued fields and $p$-adically closed valued fields. We give an effectiveness condition, related to Hensel's lemma, on a valued…

The space of constructible functions form a dense subspace of the space of generalized valuations. In this note we prove a somewhat stronger property that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of…

Products, multiplicative Chern characters, and finite coefficients, are unarguably among the most important tools in algebraic K-theory. Although they admit numerous different constructions, they are not yet fully understood at the…

Let F be the category of finite dimensional representations of an arbitrary quantum affine algebra. We prove that a tensor product $S_1\otimes ... \otimes S_N$ of simple objects of F is simple if and only if for any $i < j$, $S_i\otimes…

Let $V_1 \otimes V_2$ be a tensor product of VOAs. Using Zhu theory we discuss the theory of representations of V (associative algebra, modules and fusion rules). We prove that this theory is more or less the same as representation theory…

The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field $(K,\nu)$ and an extension $\omega$ of $\nu$ to a finite extension $L$ of $K$.…

We define a collection of tensor product norms for C*-algebras and show that a symmetric tensor product functor on the category of separable C*-algebras need not be associative.

In this paper, we propose an axiomatic definition for a tensor product categorification. A tensor product categorification is an abelian category with a categorical action of a Kac-Moody algebra g in the sense of Rouquier or Khovanov-Lauda…