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The representation theory of the group U(1,q) is discussed in detail because of its possible application in a quaternion version of the Salam-Weinberg theory. As a consequence, from purely group theoretical arguments we demonstrate that the…

High Energy Physics - Theory · Physics 2008-11-26 S. De Leo , P. Rotelli

By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…

Functional Analysis · Mathematics 2019-01-11 R. N. Gumerov , A. S. Sharafutdinov

We construct explicit approximating nets for crossed products of C*-algebras by actions of discrete quantum groups. This implies that C*-algebraic approximation properties such as nuclearity, exactness or completely bounded approximation…

Operator Algebras · Mathematics 2014-02-26 Adam Skalski , Joachim Zacharias

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

Quantum Algebra · Mathematics 2008-07-07 Yi-Zhi Huang , James Lepowsky , Lin Zhang

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

Numerical Analysis · Computer Science 2017-05-31 Qibin Zhao , Masashi Sugiyama , Andrzej Cichocki

We prove a variety results on tensor product factorizations of finite dimensional Hopf algebras (more generally Hopf algebras satisfying chain conditions in suitable braided categories). The results are analogs of well-known results on…

Rings and Algebras · Mathematics 2016-02-24 Marc Keilberg , Peter Schauenburg

Let G be a semisimple, simply-connected algebraic group over an algebraically closed field of characteristic p > 0. We observe that the tensor product of the Steinberg module with a minuscule module is always indecomposable tilting.…

Representation Theory · Mathematics 2009-09-14 S. R. Doty

Given two correspondences $X$ and $Y$ and a discrete group $G$ which acts on $X$ and coacts on $Y$, one can define a twisted tensor product $X\boxtimes Y$ which simultaneously generalizes ordinary tensor products and crossed products by…

Operator Algebras · Mathematics 2016-01-29 Adam Morgan

Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar groups can be described by a recursive…

Group Theory · Mathematics 2012-04-20 René Hartung

Let G be a finitely generated infinite pro-p group acting on a pro-p tree such that the restriction of the action to some open subgroup is free. Then we prove that G splits as a pro-p amalgamated product or as a pro-p HNN-extension over an…

Group Theory · Mathematics 2013-06-18 Wolfgang Herfort , Pavel Zalesskii , Theo Zapata

The Steinberg tensor product theorem is a fundamental result in the modular representation theory of reductive algebraic groups. It describes any finite-dimensional simple module of highest weight $\lambda$ over such a group as the tensor…

Representation Theory · Mathematics 2024-10-15 Arun S. Kannan

We explore questions of projectivity and tensor products of modules for finite dimensional Hopf algebras. We construct many classes of examples in which tensor powers of nonprojective modules are projective and tensor products of modules in…

Quantum Algebra · Mathematics 2017-06-02 Julia Yael Plavnik , Sarah Witherspoon

Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…

Machine Learning · Computer Science 2024-08-20 Milan Papež , Martin Rektoris , Tomáš Pevný , Václav Šmídl

We study glued tensor and free products of compact matrix quantum groups with cyclic groups -- so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In…

Quantum Algebra · Mathematics 2022-02-08 Daniel Gromada

Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…

Machine Learning · Computer Science 2016-11-14 Abram L. Friesen , Pedro Domingos

An abstract sampling theory associated to a unitary representation of a countable discrete non abelian group $G$, which is a semi-direct product of groups, on a separable Hilbert space is studied. A suitable expression of the data samples…

Functional Analysis · Mathematics 2018-04-16 Antonio G. García , Miguel A. Hernández-Medina , Gerardo Pérez-Villalón

The aim is the theorems of the title and the corollary that the tensor product of two free crossed resolutions of groups or groupoids is also a free crossed resolution of the product group or groupoid. The route to this corollary is through…

Algebraic Topology · Mathematics 2013-10-15 Ronald Brown , Ross Street

The goal of this paper is to extend the standard invariant-theoretic design, well-developed in the reductive case, to the setting of representation of certain non-reductive groups. This concerns the following notions and results: the…

Algebraic Geometry · Mathematics 2007-10-17 Dmitri I. Panyushev

Let $(G, P)$ be an abelian, lattice ordered group and let $X$ be a compactly aligned product system over $P$. We show that the C*-envelope of the Nica tensor algebra $\mathcal{N}\mathcal{T}^+_X$ coincides with both Sehnem's covariance…

Operator Algebras · Mathematics 2019-11-27 Adam Dor-On , Elias Katsoulis

In this article, we give a representation of bounded complex linear operators which preserve idempotent elements on the Fourier algebra of a locally compact group. When such an operator is moreover positive or contractive, we show that the…

Functional Analysis · Mathematics 2023-02-03 Ying-Fen Lin , Shiho Oi