We introduce a tensor category O+ (resp. O−) of certain modules of ĝl∞ with non-negative (resp. non-positive) integral central charges with the usual tensor product. We also introduce a tensor category (Of , ⊙ ) consisting of certain modules over GL(N) for all N . We show that the tensor categories O± and Of are semisimple abelian and all equivalent to each other. We give a formula to decompose...

The goal of this work is the presentation of some new formats which are useful for the approximation of (large and dense) matrices related to certain classes of functions and nonlocal (integral, integrodifferential) operators, especially for high-dimensional problems. These new formats elaborate on a sum of few terms of Kronecker products of smaller-sized matrices (cf. [37, 38]). In addition to...

We describe tensor product type techniques to derive robust solvers for anisotropic elliptic model problems on rectangular domains in R d. Our analysis is based on the theory of additive subspace correction methods and applies to nite-element-and prewavelet-schemes. We present multilevel-and prewavelet-based methods that are robust for anisotropic diiusion operators with additional Helmholtz te...

All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. ...

We show that the braided tensor product algebra A1⊗A2 of two module algebras A1,A2 of a quasitriangular Hopf algebraH is equal to the ordinary tensor product algebra of A1 with a subalgebra of A1⊗A2 isomorphic to A2, provided there exists a realization of H within A1. In other words, under this assumption we construct a transformation of generators which ‘decouples’ A1,A2 (i.e. makes them commu...

in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...

this paper continues the investigation of the rst author begun in part one. the hereditary properties of n-homomorphism amenability for banach algebras are investigated and the relations between n-homomorphism amenability of a banach algebra and its ide- als are found. analogous to the character amenability, it is shown that the tensor product of two unital banach algebras is n-homomorphism am...

Label propagation on the tensor product of multiple graphs can infer multi-relations among the entities across the graphs by learning labels in a tensor. However, the tensor formulation is only empirically scalable up to three graphs due to the exponential complexity of computing tensors. In this paper, we propose an optimization formulation and a scalable Lowrank Tensor-based Label Propagation...

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...