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Related papers: Spectral Triples and Generalized Crossed Products

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The subject of this article are cross product bialgebras without co-cycles. We establish a theory characterizing cross product bialgebras universally in terms of projections and injections. Especially all known types of biproduct, double…

Quantum Algebra · Mathematics 2007-05-23 Yuri N. Bespalov , Bernhard Drabant

It is probably safe to say that just about everyone reading this article is familiar with the cross product and the dot product. However, what many readers may not be aware of is that the familiar properties of the cross product in three…

History and Overview · Mathematics 2013-11-01 Peter F. McLoughlin

Given a group $G$ and a partial factor set $\sigma $ of $G,$ we introduce the twisted partial group algebra $\kappa_{par}^{\sigma}G,$ which governs the partial projective $\sigma$-representations of $G$ into algebras over a filed $\kappa.$…

Rings and Algebras · Mathematics 2023-11-29 Mikhailo Dokuchaev , Emmanuel Jerez

We show how the known theory of noncommutative Orlicz spaces for semifinite von Neumann algebras equipped with an fns trace, may be recovered using crossed product techniques. Then using this as a template, we construct analogues of such…

Operator Algebras · Mathematics 2013-06-14 Louis Labuschagne

In this paper, we define the bimetric spectral Einstein-Hilbert action which generalizes the spectral Einstein-Hilbert action. We compute the bimetric spectral Einstein-Hilbert action for the Lorentz warped product. Thus, we get the…

Differential Geometry · Mathematics 2025-02-11 Siyao Liu , Yong Wang

multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…

Numerical Analysis · Mathematics 2007-05-23 Stefano Serra Capizzano

For any maximal coaction (A, G, delta) and any closed normal subgroup N of G, there exists an imprimitivity bimodule Y between the full crossed product A x G x N and A x G/N, together with a compatible coaction delta_Y of G. The assignment…

Operator Algebras · Mathematics 2007-05-23 S. Kaliszewski , John Quigg

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed.

Operator Algebras · Mathematics 2021-03-03 Valeriano Aiello , Daniele Guido , Tommaso Isola

We study quantum integrable models with GL(3) trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of the highest…

Mathematical Physics · Physics 2015-06-17 S. Pakuliak , E. Ragoucy , N. A. Slavnov

We establish relations between representation dimensions of two algebras connected by a Frobenius bimodule or extension. Consequently, upper bounds and equality formulas for representation dimensions of group algebras, symmetric separably…

Representation Theory · Mathematics 2020-08-13 Changchang Xi

The main properties of the crossed product in the category of Hopf algebras are investigated. Let $A$ and $H$ be two Hopf algebras connected by two morphism of coalgebras $\triangleright : H\ot A \to A$, $f:H\ot H\to A$. The crossed product…

Quantum Algebra · Mathematics 2014-02-24 A. L. Agore

We provide sufficient conditions to factorise an equivariant spectral triple as a Kasparov product of unbounded classes constructed from the group action on the algebra and from the fixed point spectral triple. Our results are for the…

K-Theory and Homology · Mathematics 2015-05-13 Iain Forsyth , Adam Rennie

We consider Hopf bimodules and crossed modules over a Hopf algebra $H$ in a braided category. They are the key-stones for braided bicovariant differential calculi and their invariant vector fields respectively, as well as for the…

q-alg · Mathematics 2008-02-03 Yuri Bespalov , Bernhard Drabant

In this paper, we mainly provide a new approache to construct Hom-Hopf algebras. For this, we introduce and study the notion of a left $(m,k)$-Hom-crossed product structure as a generalization of $k$-Hom-smash product structure. Then one…

Rings and Algebras · Mathematics 2025-10-21 Botong Gai , Shuanhong Wang

A pair of disjoint lines on a smooth cubic threefold determines an irreducible component of the Hilbert scheme. We prove that this component is smooth and isomorphic to the blow-up of the symmetric product of Fano varieties of lines on the…

Algebraic Geometry · Mathematics 2025-04-22 Yilong Zhang

It is well-known that characters classify linear representations of finite groups, that is if characters of two representations of a finite group are the same, these representations are equivalent. It is also well-known that, in general,…

Group Theory · Mathematics 2024-03-14 Michael Stessin

Let H be a complex Hilbert space, B(H) and S(H) be the spaces of all bounded operators and all self-adjoint operators on H, respectively. We give the concrete forms of the maps on B(H) and also S(H) which preserve the spectrum of certain…

Functional Analysis · Mathematics 2013-09-17 Ali Taghavi , Roja Hosseinzadeh

This paper primarily investigates spectral properties of symmetric tensor products of Hilbert-space operators. For a unilateral weighted shift operator $S_w$, we present an algorithm to compute the point spectrum of its symmetric and…

Functional Analysis · Mathematics 2025-09-10 Yuchi Yang , Yuanhang Zhang

In this work we present a new definition to the Partial Crossed Product by actions of inverse semigroups in a C^*-algebra, without using the covariant representations as Sieben did in [5]. Also we present an isomorphism between the partial…

Operator Algebras · Mathematics 2008-05-26 Ruy Exel , Felipe Vieira

A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with…

Operator Algebras · Mathematics 2011-03-31 Ami Viselter