covariant representations
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Author(s):  
Boyu Li

We establish a Wold-type decomposition for isometric and isometric Nica-covariant representations of the odometer semigroup. These generalize the Wold-type decomposition for commuting pairs of isometries due to Popovici and for pairs of doubly commuting isometries due to Słociński.


2020 ◽  
Vol 549 ◽  
pp. 1-94
Author(s):  
Daniel Beltiţă ◽  
Hendrik Grundling ◽  
Karl-Hermann Neeb

2018 ◽  
Vol 33 (08) ◽  
pp. 1830007 ◽  
Author(s):  
Ion I. Cotaescu

The properties of the covariant quantum fields on de Sitter space–times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the [Formula: see text] group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.


2018 ◽  
Vol 33 (04) ◽  
pp. 1850026 ◽  
Author(s):  
Ion I. Cotăescu

The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity.


2013 ◽  
Vol 65 (4) ◽  
pp. 768-782 ◽  
Author(s):  
Adam Hanley Fuller

AbstractLet S be the semigroup S = Σ⊕ki∈1 Si, where for each i∈ I, Si is a countable subsemigroup of the additive semigroup R+ containing 0. We consider representations of S as contractions {Ts} s∈S on a Hilbert space with the Nica-covariance property: T*s Tt = TtT*s whenever t^s = 0. We show that all such representations have a unique minimal isometric Nica-covariant dilation.This result is used to help analyse the nonself-adjoint semicrossed product algebras formed from Nica-covariant representations of the action of S on an operator algebra A by completely contractive endomorphisms. We conclude by calculating the C*-envelope of the isometric nonself-adjoint semicrossed product algebra (in the sense of Kakariadis and Katsoulis).


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