scholarly journals Iterated crossed products

2014 ◽  
Vol 13 (07) ◽  
pp. 1450036 ◽  
Author(s):  
Florin Panaite
Keyword(s):  
Tensor Product ◽  
Crossed Product ◽  
Smash Product ◽  
Algebra Structure ◽  
Crossed Products ◽  
Twisted Tensor Product

We define a "mirror version" of Brzeziński's crossed product and we prove that, under certain circumstances, a Brzeziński crossed product D ⊗R,σ V and a mirror version [Formula: see text] may be iterated, obtaining an algebra structure on W ⊗ D ⊗ V. Particular cases of this construction are the iterated twisted tensor product of algebras and the quasi-Hopf two-sided smash product.

scholarly journals TENSOR-PRODUCT COACTION FUNCTORS

2020 ◽  
pp. 1-16
Author(s):  
S. KALISZEWSKI ◽  
MAGNUS B. LANDSTAD ◽  
JOHN QUIGG
Keyword(s):  
Tensor Product ◽  
Recent Work ◽  
Analogous Result ◽  
Crossed Product ◽  
Discrete Groups ◽  
Crossed Products ◽  
Fixed Action ◽  
Product Action ◽  
K Theory

Recent work by Baum et al. [‘Expanders, exact crossed products, and the Baum–Connes conjecture’, Ann. K-Theory 1(2) (2016), 155–208], further developed by Buss et al. [‘Exotic crossed products and the Baum–Connes conjecture’, J. reine angew. Math. 740 (2018), 111–159], introduced a crossed-product functor that involves tensoring an action with a fixed action $(C,\unicode[STIX]{x1D6FE})$ , then forming the image inside the crossed product of the maximal-tensor-product action. For discrete groups, we give an analogue for coaction functors. We prove that composing our tensor-product coaction functor with the full crossed product of an action reproduces their tensor-crossed-product functor. We prove that every such tensor-product coaction functor is exact, and if $(C,\unicode[STIX]{x1D6FE})$ is the action by translation on $\ell ^{\infty }(G)$ , we prove that the associated tensor-product coaction functor is minimal, thereby recovering the analogous result by the above authors. Finally, we discuss the connection with the $E$ -ization functor we defined earlier, where $E$ is a large ideal of $B(G)$ .

scholarly journals TWISTING OPERATORS, TWISTED TENSOR PRODUCTS AND SMASH PRODUCTS FOR HOM-ASSOCIATIVE ALGEBRAS

2015 ◽  
Vol 58 (3) ◽  
pp. 513-538 ◽  
Author(s):  
ABDENACER MAKHLOUF ◽  
FLORIN PANAITE
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Smash Product ◽  
Associative Algebras ◽  
Common Generalization ◽  
Twisted Tensor Product

AbstractThe purpose of this paper is to provide new constructions of Hom-associative algebras using Hom-analogues of certain operators called twistors and pseudotwistors, by deforming a given Hom-associative multiplication into a new Hom-associative multiplication. As examples, we introduce Hom-analogues of the twisted tensor product and smash product. Furthermore, we show that the construction by the twisting principle introduced by Yau and the twisting of associative algebras using pseudotwistors admit a common generalization.

scholarly journals L-R-Smash Products and L-R-Twisted Tensor Products of Algebras

2014 ◽  
Vol 21 (01) ◽  
pp. 129-146 ◽  
Author(s):  
Mădălin Ciungu ◽  
Florin Panaite
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Smash Product ◽  
Common Generalization ◽  
New Construction ◽  
Twisted Tensor Product

We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for instance, we prove a result of the type “invariance under twisting” and we show that under certain circumstances L-R-twisted tensor products of algebras may be iterated.

scholarly journals Characteristic invatiant of tensor product actions and actions on crossed products

2002 ◽  
Vol 73 (3) ◽  
pp. 357-376
Author(s):  
Yukako Miwa ◽  
Yoshikazu Katayama
Keyword(s):  
Tensor Product ◽  
Discrete Group ◽  
Product Formula ◽  
Crossed Product ◽  
Crossed Products ◽  
Modular Invariant ◽  
Characteristic Invariant ◽  
Extended Action ◽  
Product Action

AbstractThe first purpose of this paper is to give a tensor product formula of the characteristic invariant and modular invariant for a tensor product action of a discrete group G on AFD factors. The second purpose is to describe a characteristic invariant and modular invariant of the extended action to a crossed product in terms of the original invariants.

scholarly journals The Dixmier-Douady class of groupoid crossed products

2004 ◽  
Vol 76 (2) ◽  
pp. 223-234 ◽  
Author(s):  
Paul S. Muhly ◽  
Dana P. Williams
Keyword(s):  
Crossed Product ◽  
Crossed Products ◽  
Continuous Trace

AbstractWe give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of elementary C*-algebras that satisfies Fell's condition.

scholarly journals A rigidity result for crossed products of actions of Baumslag–Solitar groups

2015 ◽  
Vol 26 (14) ◽  
pp. 1550117
Author(s):  
Niels Meesschaert
Keyword(s):  
Probability Measure ◽  
Free Probability ◽  
Crossed Product ◽  
Crossed Products ◽  
Orbit Equivalence ◽  
Rigidity Result ◽  
Profinite Completions ◽  
Abelian Subgroups ◽  
Measure Equivalence ◽  
Measure Preserving Actions

Let [Formula: see text] and [Formula: see text] be two ergodic essentially free probability measure preserving actions of nonamenable Baumslag–Solitar groups whose canonical almost normal abelian subgroups act aperiodically. We prove that an isomorphism between the corresponding crossed product II1 factors forces [Formula: see text] when [Formula: see text] and [Formula: see text] when [Formula: see text]. This improves an orbit equivalence rigidity result obtained by Houdayer and Raum in [Baumslag–Solitar groups, relative profinite completions and measure equivalence rigidity, J. Topol. 8 (2015) 295–313].

Morita equivalences between fixed point algebras and crossed products

1999 ◽  
Vol 125 (1) ◽  
pp. 43-52 ◽  
Author(s):  
CHI-KEUNG NG
Keyword(s):  
Fixed Point ◽  
Quantum Group ◽  
Type Theorem ◽  
Compact Quantum Group ◽  
Crossed Product ◽  
Crossed Products ◽  
Morita Equivalent ◽  
Fixed Point Algebra

In this paper, we will prove that if A is a C*-algebra with an effective coaction ε by a compact quantum group, then the fixed point algebra and the reduced crossed product are Morita equivalent. As an application, we prove an imprimitivity type theorem for crossed products of coactions by discrete Kac C*-algebras.

scholarly journals Extension problems and non-Abelian duality for C*-algebras

2007 ◽  
Vol 75 (2) ◽  
pp. 229-238 ◽  
Author(s):  
Astrid an Huef ◽  
S. Kaliszewski ◽  
Iain Raeburn
Keyword(s):  
Compact Group ◽  
Unitary Representation ◽  
Closed Subgroup ◽  
Locally Compact Group ◽  
Crossed Product ◽  
Crossed Products ◽  
Test Question ◽  
Locally Compact ◽  
Dual Representation ◽  
C Algebras

Suppose that H is a closed subgroup of a locally compact group G. We show that a unitary representation U of H is the restriction of a unitary representation of G if and only if a dual representation Û of a crossed product C*(G) ⋊ (G/H) is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-Abelian duality for crossed products of C*-algebras.

scholarly journals Discrete product systems with twisted units

1995 ◽  
Vol 52 (2) ◽  
pp. 317-326 ◽  
Author(s):  
Marcelo Laca
Keyword(s):  
Dynamical System ◽  
Crossed Product ◽  
Type I ◽  
Crossed Products ◽  
Product System ◽  
C Algebra ◽  
Covariant Representations ◽  
Product Systems ◽  
Recent Theorem ◽  
I Factor

The spectral C*-algebra of the discrete product systems of H.T. Dinh is shown to be a twisted semigroup crossed product whenever the product system has a twisted unit. The covariant representations of the corresponding dynamical system are always faithful, implying the simplicity of these crossed products; an application of a recent theorem of G.J. Murphy gives their nuclearity. Furthermore, a semigroup of endomorphisms of B(H) having an intertwining projective semigroup of isometries can be extended to a group of automorphisms of a larger Type I factor.

scholarly journals Crossed Products and Ramification

1966 ◽  
Vol 28 ◽  
pp. 85-111 ◽  
Author(s):  
Susan Williamson
Keyword(s):  
Galois Group ◽  
Galois Extension ◽  
Valuation Ring ◽  
Field Extension ◽  
Integral Closure ◽  
Crossed Product ◽  
Crossed Products ◽  
Quotient Field ◽  
Rank One ◽  
Definition Of

Introduction. Let S be the integral closure of a complete discrete rank one valuation ring R in a finite Galois extension of the quotient field of R, and let G denote the Galois group of the quotient field extension. Auslander and Rim have shown in [3] that the trivial crossed product Δ (1, S, G) is an hereditary order if and only if 5 is a tamely ramified extension of R. And the author has proved in [7] that if the extension S of R is tamely ramified then the crossed product Δ(f, 5, G) is a Π-principal hereditary order for each 2-cocycle f in Z2(G, U(S)). (See Section 1 for the definition of Π-principal hereditary order.) However, the author has exhibited in [8] an example of a crossed product Δ(f, S, G) which is a Π-principal hereditary order in the case when S is a wildly ramified extension of R.

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