scholarly journals A basis for the GLn tensor product algebra

2005 ◽  
Vol 196 (2) ◽  
pp. 531-564 ◽  
Author(s):  
Roger E. Howe ◽  
Eng-Chye Tan ◽  
Jeb F. Willenbring
Keyword(s):  
Tensor Product ◽  
Product Algebra

scholarly journals On the structures of hive algebras and tensor product algebras for general linear groups of low rank

2019 ◽  
Vol 29 (07) ◽  
pp. 1193-1218
Author(s):  
Donggyun Kim ◽  
Sangjib Kim ◽  
Euisung Park
Keyword(s):  
Tensor Product ◽  
Irreducible Polynomial ◽  
Tensor Products ◽  
Low Rank ◽  
General Linear ◽  
Generators And Relations ◽  
General Linear Groups ◽  
Highest Weight ◽  
Polynomial Representations ◽  
Product Algebra

The tensor product algebra [Formula: see text] for the complex general linear group [Formula: see text], introduced by Howe et al., describes the decomposition of tensor products of irreducible polynomial representations of [Formula: see text]. Using the hive model for the Littlewood–Richardson (LR) coefficients, we provide a finite presentation of the algebra [Formula: see text] for [Formula: see text] in terms of generators and relations, thereby giving a description of highest weight vectors of irreducible representations in the tensor products. We also compute the generating function of certain sums of LR coefficients.

scholarly journals A Generalization for n-Cocycles

ISRN Algebra ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Beishang Ren ◽  
Shixun Lin
Keyword(s):  
Tensor Product ◽  
Type Ii ◽  
Module Algebra ◽  
Product Algebra

We will give generalized definitions called type II n-cocycles and weak quasi-bialgebra and also show properties of type II n-cocycles and some results about weak quasi-bialgebras, for instance, construct a new structure of tensor product algebra over a module algebra on weak quasi-bialgebras.

scholarly journals TOPOLOGICAL STABLE RANK OF INCLUSIONS OF UNITAL C*-ALGEBRAS

2006 ◽  
Vol 17 (01) ◽  
pp. 19-34 ◽  
Author(s):  
HIROYUKI OSAKA ◽  
TAMOTSU TERUYA
Keyword(s):  
Finite Group ◽  
Tensor Product ◽  
Finite Type ◽  
Stable Rank ◽  
C Algebras ◽  
Rank One ◽  
Topological Stable Rank ◽  
Crossed Product Algebra ◽  
A Finite Group ◽  
Product Algebra

Let 1 ∈ A ⊂ B be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute the topological stable rank of B (= tsr (B)) when A has topological stable rank one. We show that tsr (B) ≤ 2 when A is a tsr boundedly divisible algebra, in particular, A is a C*-minimal tensor product UHF ⊗ D with tsr (D) = 1. When G is a finite group and α is an action of G on UHF, we know that a crossed product algebra UHF ⋊α G has topological stable rank less than or equal to two. These results are affirmative data to a generalization of a question by Blackadar in 1988.

Spectra for Infinite Tensor Product Type Actions of Compact Groups

1996 ◽  
Vol 48 (2) ◽  
pp. 330-342
Author(s):  
Elliot C. Gootman ◽  
Aldo J. Lazar
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Abelian Groups ◽  
Product Type ◽  
Crossed Product ◽  
Compact Groups ◽  
Ideal Structure ◽  
Crossed Product Algebra ◽  
Product Algebra ◽  
The Ideal

AbstractWe present explicit calculations of the Arveson spectrum, the strong Arveson spectrum, the Connes spectrum, and the strong Connes spectrum, for an infinite tensor product type action of a compact group. Using these calculations and earlier results (of the authors and C. Peligrad) relating the various spectra to the ideal structure of the crossed product algebra, we prove that the topology of G influences the ideal structure of the crossed product algebra, in the following sense: if G contains a nontrivial connected group as a direct summand, then the crossed product algebra may be prime, but it is never simple; while if G is discrete, the crossed product algebra is simple if and only if it is prime. These results extend to compact groups analogous results of Bratteli for abelian groups. In addition, we exhibit a class of examples illustrating that for compact groups, unlike the case for abelian groups, the Connes spectrum and strong Connes spectrum need not be stable.

QUASITRIANGULARITY OF BRZEZIŃSKI'S CROSSED COPRODUCTS

2011 ◽  
Vol 10 (02) ◽  
pp. 241-255 ◽  
Author(s):  
TIANSHUI MA ◽  
HAIYING LI ◽  
SHUANHONG WANG
Keyword(s):  
Hopf Algebra ◽  
Tensor Product ◽  
Recent Work ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Algebra Structure ◽  
Product Algebra ◽  
Necessary And Sufficient ◽  
Crossed Coproducts ◽  
Quasitriangular Hopf Algebra

In continuation of our recent work about the quasitriangular structures for the twisted tensor biproduct, we give the necessary and sufficient conditions for Brzeziński crossed coproduct coalgebra, including the twisted tensor coproduct introduced by Caenepeel, Ion, Militaru and Zhu and crossed coproduct as constructed by Lin, equipped with the usual tensor product algebra structure to be a Hopf algebra. Furthermore, the necessary and sufficient conditions for Brzeziński crossed coproduct to be a quasitriangular Hopf algebra are obtained.

UNBRAIDING TRANSFORMATIONS FOR BRAIDED TENSOR FACTORS

2001 ◽  
Vol 16 (04n06) ◽  
pp. 261-267 ◽  
Author(s):  
GAETANO FIORE ◽  
HAROLD STEINACKER ◽  
JULIUS WESS
Keyword(s):  
Tensor Product ◽  
Quantum Group ◽  
Covariant Quantum ◽  
Heisenberg Algebras ◽  
Product Algebra

Two quantum group covariant algebras [Formula: see text] can be embedded in a larger one through the so-called braided tensor product, whereby they do not commute with each other. We briefly report on our transformations of generators8 which allow to express this braided tensor product algebra as an ordinary tensor product algebra of [Formula: see text] with a subalgebra isomorphic to [Formula: see text] and commuting with [Formula: see text]. The construction of the transformations is based on the existence of a realization of H within [Formula: see text]. We apply the results to the braided tensor product algebras of two or more quantum group covariant quantum spaces or deformed Heisenberg algebras.

Reference Signal Based Tensor Product Expansion for EOG-Related Artifact Separation in EEG

2017 ◽  
Vol E100.A (11) ◽  
pp. 2230-2237
Author(s):  
Akitoshi ITAI ◽  
Arao FUNASE ◽  
Andrzej CICHOCKI ◽  
Hiroshi YASUKAWA
Keyword(s):  
Tensor Product ◽  
Reference Signal

On degeneracy problem of NFSRs via semi-tensor product

2020 ◽  
Author(s):  
Xinyu Zhao ◽  
Biao Wang ◽  
Shuqian Zhu ◽  
Jun-e Feng
Keyword(s):  
Tensor Product ◽  
Degeneracy Problem

On the Buchstaber Subring in MSp∗

1998 ◽  
Vol 5 (5) ◽  
pp. 401-414
Author(s):  
M. Bakuradze
Keyword(s):  
Tensor Product ◽  
Characteristic Classes ◽  
Generalized Quaternion ◽  
Symplectic Cobordisms

Abstract A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.

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