The structure of the observable algebra determined by a Hopf *-subalgebra in Hopf spin models

Let H be a finite dimensional Hopf C*-algebra, H1 a Hopf*-subalgebra of H. This paper focuses on the observable algebra AH1 determined by H1 in nonequilibrium Hopf spin models, in which there is a copy of H1 on each lattice site, and a copy of ? on each link, where ? denotes the dual of H. Furthermore, using the iterated twisted tensor product of finite +*-algebras, one can prove that the observable algebraAH1 is *-isomorphic to the C*-inductive limit ... o H1 o ? o H1 o ? o H1 o ... .

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

The 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.

The twisted Cartesian model for the double path fibration

In this paper, the notion of a truncating twisting function from a cubical set to a permutahedral set and the corresponding notion of a twisted Cartesian product of these sets are introduced. The latter becomes a permutocubical set that models, in particular, the path fibration on a loop space. The chain complex of this twisted Cartesian product is in fact a comultiplicative twisted tensor product of cubical chains of base and permutahedral chains of fibre. This construction is formalized as a theory of twisted tensor products for Hirsch algebras.

Iterated crossed products

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.

QUANTUM GROUP-TWISTED TENSOR PRODUCTS OF C*-ALGEBRAS

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.

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

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.

TWISTED TENSOR PRODUCT MODULES OVER MÖBIUS TWISTED TENSOR PRODUCT NONLOCAL VERTEX ALGEBRAS

This is the third part in a series of papers developing a twisted tensor product theory for nonlocal vertex algebras and its modules. In this paper we introduce and study twisted tensor product modules over Möbius twisted tensor product nonlocal vertex algebras. Among the main results, we find the isomorphic relation between the opposite Möbius twisted tensor product nonlocal vertex algebra and twisted tensor product of opposite Möbius nonlocal vertex algebras. And we also establish the isomorphism between two twisted tensor product contragredient modules. Furthermore, we study iterated twisted tensor product modules over iterated twisted tensor product nonlocal vertex algebras and find conditions for constructing an iterated twisted tensor product module of three factors.