scholarly journals The maximal quantum group-twisted tensor product of C*-algebras

2018 ◽  
Vol 12 (1) ◽  
pp. 279-330 ◽  
Author(s):  
Sutanu Roy ◽  
Thomas Timmermann
Keyword(s):  
Tensor Product ◽  
Quantum Group ◽  
C Algebras ◽  
Twisted Tensor Product

scholarly journals QUANTUM GROUP-TWISTED TENSOR PRODUCTS OF C*-ALGEBRAS

2014 ◽  
Vol 25 (02) ◽  
pp. 1450019 ◽  
Author(s):  
RALF MEYER ◽  
SUTANU ROY ◽  
STANISŁAW LECH WORONOWICZ
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Quantum Group ◽  
Quantum Groups ◽  
Tensor Products ◽  
Group Representations ◽  
Basic Properties ◽  
C Algebras ◽  
Twisted Tensor Product

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways, based on certain pairs of quantum group representations and based on covariant Hilbert space representations, respectively. We establish basic properties of the twisted tensor product and study some examples.

scholarly journals Nuclear subalgebras of UHF C*-algebras

1986 ◽  
Vol 29 (1) ◽  
pp. 97-100 ◽  
Author(s):  
R. J. Archbold ◽  
Alexander Kumjian
Keyword(s):  
Tensor Product ◽  
Inductive Limit ◽  
Inductive Limits ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
The Family ◽  
Algebraic Tensor Product

A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified in terms of the invariant K0 [7], [5].

Cartan's constructions and the twisted Eilenberg–Zilber theorem

2010 ◽  
Vol 17 (1) ◽  
pp. 13-23
Author(s):  
Víctor Álvarez ◽  
José Andrés Armario ◽  
María Dolores Frau ◽  
Pedro Real
Keyword(s):  
Perturbation Theory ◽  
Tensor Product ◽  
Cartesian Product ◽  
Tensor Products ◽  
Standard Product ◽  
Homological Perturbation Theory ◽  
Twisted Tensor Product ◽  
Homological Perturbation ◽  
Twisted Cartesian Product

Abstract Let 𝐺 × τ 𝐺′ be the principal twisted Cartesian product with fibre 𝐺, base 𝐺 and twisting function where 𝐺 and 𝐺′ are simplicial groups as well as 𝐺 × τ 𝐺′; and 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁 (𝐺′) be the twisted tensor product associated to 𝐶𝑁 (𝐺 × τ 𝐺′) by the twisted Eilenberg–Zilber theorem. Here we prove that the pair 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁(𝐺′), μ) is a multiplicative Cartan's construction where μ is the standard product on 𝐶𝑁(𝐺) ⊗ 𝐶𝑁(𝐺′). Furthermore, assuming that a contraction from 𝐶𝑁(𝐺′) to 𝐻𝐺′ exists and using the techniques from homological perturbation theory, we extend the former result to other “twisted” tensor products of the form 𝐶𝑁(𝐺) ⊗ 𝐻𝐺′.

scholarly journals Multivariableq-Hahn polynomials as coupling coefficients for quantum algebra representations

2001 ◽  
Vol 28 (6) ◽  
pp. 331-358 ◽  
Author(s):  
Hjalmar Rosengren
Keyword(s):  
Tensor Product ◽  
Quantum Group ◽  
Quantum Algebra ◽  
Coupling Coefficients ◽  
Highest Weight ◽  
Hahn Polynomials ◽  
Highest Weight Representations

We study coupling coefficients for a multiple tensor product of highest weight representations of theSU(1,1)quantum group. These are multivariable generalizations of theq-Hahn polynomials.

scholarly journals INVOLUTION AND THE HAAGERUP TENSOR PRODUCT

2001 ◽  
Vol 44 (2) ◽  
pp. 317-322 ◽  
Author(s):  
Ajay Kumar
Keyword(s):  
Tensor Product ◽  
Banach Algebra ◽  
Subject Classification ◽  
Primary 46L05 ◽  
C Algebras

AbstractWe show that the involution $\theta(a\otimes b)=a^*\otimes b^*$ on the Haagerup tensor product $A\otimes_{\mrm{H}}B$ of $C^*$-algebras $A$ and $B$ is an isometry if and only if $A$ and $B$ are commutative. The involutive Banach algebra $A\otimes_{\mrm{H}}A$ arising from the involution $a\otimes b\to b^*\otimes a^*$ is also studied.AMS 2000 Mathematics subject classification: Primary 46L05; 46M05

Approximating maps and exact C*-algebras

1982 ◽  
Vol 91 (2) ◽  
pp. 285-289 ◽  
Author(s):  
R. J. Archbold
Keyword(s):  
Tensor Product ◽  
Linear Mapping ◽  
Extra Condition ◽  
Bounded Linear ◽  
C Algebras ◽  
The Right

Let A and E be C*-algebras, let A ⊗ B denote the minimal C*-tensor product, and let ε A *. The right slice map R: A ⊗ B → B is the unique bounded linear mapping with the property that R (a ⊗ b) = (a)b (a ε A, b ε B)(10). A triple (A, B, D), where D is a C*-subalgebra of B, is said to have the slice map property if whenever x ε A ⊗ B and R(x) D for all ε A* then x ε A ⊗ D). It is known that (A, B, D) has the slice map property whenever A is nuclear (11,13), but it appears to be still unknown whether the nuclearity of B will suffice (unless some extra condition is placed on D (l)).

Elementary operators and subhomogeneous C*-algebras

2010 ◽  
Vol 54 (1) ◽  
pp. 99-111 ◽  
Author(s):  
Ilja Gogić
Keyword(s):  
Tensor Product ◽  
Finite Type ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
C Algebras ◽  
Direct Sum ◽  
Elementary Operators ◽  
Uniformly Bounded

AbstractLet A be a C*-algebra and let ΘA be the canonical contraction form the Haagerup tensor product of M(A) with itself to the space of completely bounded maps on A. In this paper we consider the following conditions on A: (a) A is a finitely generated module over the centre of M(A); (b) the image of ΘA is equal to the set E(A) of all elementary operators on A; and (c) the lengths of elementary operators on A are uniformly bounded. We show that A satisfies (a) if and only if it is a finite direct sum of unital homogeneous C*-algebras. We also show that if a separable A satisfies (b) or (c), then A is necessarily subhomogeneous and the C*-bundles corresponding to the homogeneous subquotients of A must be of finite type.

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