相关论文: On tensor products of operator modules

Tensor product of irreducible modules of highest weight over a semi-simple quantum group is semi-simple if and only if a natural contravariant form is non-degenerate when restricted to the span of singular vectors. We express this…

We provide a unified treatment of several commuting tensor products considered in the literature, including the tensor product of enriched categories and the Boardman-Vogt tensor product of operads and symmetric multicategories, subsuming…

In the references [HL1]--[HL5] and [H1], a theory of tensor products of modules for a vertex operator algebra is being developed. To use this theory, one first has to verify that the vertex operator algebra satisfies certain conditions. We…

We construct classes of von Neumann algebra modules by considering ``column sums" of noncommutative L^p spaces. Our abstract characterization is based on an L^{p/2}-valued inner product, thereby generalizing Hilbert C*-modules and…

In this work we introduce the notions of Peiffer product and Peiffer commutator of internal pre-crossed modules over a fixed object B, extending the corresponding classical notions to any semi-abelian category C. We prove that, under mild…

Let C be a coalgebra over a field k and A its dual algebra. The category of C-comodules is equivalent to a category of A-modules. We use this to interpret the cotensor product M \square N of two comodules in terms of the appropriate…

We study bounded bilinear maps on a C$^*$-algebra $A$ having product property at $c\in A$. This leads us to the question of when a C$^*$-algebra is determined by products at $c.$ In the first part of our paper, we investigate this question…

For unital $C^*$-algebras $A$ and $B$, we completely characterize the isometric ($*$-) automorphisms of their Banach space projective tensor product $A\otimes^\gamma B$. This leads to the characterization of inner and outer isometric…

In this paper I consider the polymorpism of representations of universal algebra and tensor product of representations of universal algebra.

For $C^*$-algebras $A$ and $B$, we study the bi-continuity of the canonical embedding of $A^{**}\ot_{\gamma} B^{**}$ ($A^{**}\hat{\ot} B^{**}$) into $(A \ot_{\gamma} B)^{**}$ (resp. $(A \hat{\ot} B)^{**}$), and its isomorphism. Ideal…

We study a mixed tensor product $\mathbf{3}^{\otimes m} \otimes \mathbf{\overline{3}}^{\otimes n}$ of the three-dimensional fundamental representations of the Hopf algebra $U_{q} s\ell(2|1)$, whenever $q$ is not a root of unity. Formulas…

Every cluster-tilted algebra $B$ is the relation extension $C\ltimes \text{Ext}^2_C(DC,C)$ of a tilted algebra $C$. A $B$-module is called induced if it is of the form $M\otimes_C B$ for some $C$-module $M$. We study the relation between…

We apply the general theory of tensor products of modules for a vertex operator algebra developed in our papers hep-th/9309076, hep-th/9309159, hep-th/9401119, q-alg/9505018, q-alg/9505019 and q-alg/9505020 to the case of the…

We prove that the multiplication map L^a(M)\otimes_M L^b(M)\to L^{a+b}(M) is an isometric isomorphism of (quasi)Banach M-M-bimodules. Here L^a(M)=L_{1/a}(M) is the noncommutative L_p-space of an arbitrary von Neumann algebra M and \otimes_M…

For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g. level one in type A) which becomes in the limit (for anti-dominant weights) the…

Recall that an algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that if L is a component of the (stable)…

The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…

Let $A$ and $B$ be commutative semisimple Banach algebras. In this paper, the $BSE$ and $BED$- property of tensor Banach algebra $A{\otimes}_{\gamma} B$ with respect to the Banach algebras $A$ and $B$ are assesed. In particular, $BSE$ and…

Imprimitivity theorems provide a fundamental tool for studying the representation theory and structure of crossed-product C*-algebras. In this work, we show that the Imprimitivity Theorem for induced algebras, Green's Imprimitivity Theorem…

Let $G$ be a discrete group acting on a von Neumann algebra $M$ by properly outer $*$-automorphisms. In this paper we study the containment $M \subseteq M\rtimes_\alpha G$ of $M$ inside the crossed product. We characterize the intermediate…