Group graded Morita equivalences for wreath products

AbstractEvery tropical ideal in the sense of Maclagan–Rincón has an associated tropical variety, a finite polyhedral complex equipped with positive integral weights on its maximal cells. This leads to the realisability question, ubiquitous in tropical geometry, of which weighted polyhedral complexes arise in this manner. Using work of Las Vergnas on the non-existence of tensor products of matroids, we prove that there is no tropical ideal whose variety is the Bergman fan of the direct sum of the Vámos matroid and the uniform matroid of rank two on three elements and in which all maximal cones have weight one.

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Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2021.9 ◽

2021 ◽

pp. 1-36

Author(s):

ARIE LEVIT ◽

ALEXANDER LUBOTZKY

Keyword(s):

Ergodic Theorem ◽

Abelian Groups ◽

Wreath Products ◽

Finitely Generated ◽

Metabelian Groups ◽

Amenable Groups ◽

Pointwise Ergodic Theorem ◽

Lamplighter Group ◽

Invariant Random Subgroups

Abstract We prove that all invariant random subgroups of the lamplighter group L are co-sofic. It follows that L is permutation stable, providing an example of an infinitely presented such group. Our proof applies more generally to all permutational wreath products of finitely generated abelian groups. We rely on the pointwise ergodic theorem for amenable groups.

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The dual of the space of bounded operators on a Banach space

Concrete Operators ◽

10.1515/conop-2020-0109 ◽

2021 ◽

Vol 8 (1) ◽

pp. 48-59

Author(s):

Fernanda Botelho ◽

Richard J. Fleming

Keyword(s):

Banach Space ◽

Tensor Product ◽

Banach Spaces ◽

Dual Space ◽

Tensor Products ◽

Bounded Operators ◽

Projective Tensor Product ◽

Projective Tensor

Abstract Given Banach spaces X and Y, we ask about the dual space of the 𝒧(X, Y). This paper surveys results on tensor products of Banach spaces with the main objective of describing the dual of spaces of bounded operators. In several cases and under a variety of assumptions on X and Y, the answer can best be given as the projective tensor product of X ** and Y *.

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κ -Poincaré comodules, braided tensor products, and noncommutative quantum field theory

Physical Review D ◽

10.1103/physrevd.103.126009 ◽

2021 ◽

Vol 103 (12) ◽

Author(s):

Fedele Lizzi ◽

Flavio Mercati

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Tensor Products ◽

Quantum Field ◽

Noncommutative Quantum Field Theory ◽

Noncommutative Quantum

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Spectra of elements in operator space tensor products of $$\hbox {C}^*$$-algebras

Positivity ◽

10.1007/s11117-021-00856-z ◽

2021 ◽

Author(s):

Janson Antony ◽

Ajay Kumar

Keyword(s):

Tensor Products ◽

Operator Space ◽

C Algebras ◽

Space Tensor

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RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s1474748021000165 ◽

2021 ◽

pp. 1-37

Author(s):

Martijn Caspers

Keyword(s):

Quantum Group ◽

Quantum Groups ◽

Riesz Transform ◽

Wreath Products ◽

Compact Quantum Group ◽

Riesz Transforms ◽

Markov Semigroup ◽

Markov Semigroups ◽

Free Products ◽

Compact Quantum Groups

Abstract One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups of central multipliers on a compact quantum group which we shall call ‘approximate linearity with almost commuting intertwiners’. We show that this property is stable under free products, monoidal equivalence, free wreath products and dual quantum subgroups. Examples include in particular all the (higher-dimensional) free orthogonal easy quantum groups. We then show that a compact quantum group with a quantum Markov semigroup that is approximately linear with almost commuting intertwiners satisfies the immediately gradient- ${\mathcal {S}}_2$ condition from [10] and derive strong solidity results (following [10]). Using the noncommutative Riesz transform we also show that these quantum groups have the Akemann–Ostrand property; in particular, the same strong solidity results follow again (now following [27]).

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SUBPROJECTIVITY OF PROJECTIVE TENSOR PRODUCTS OF BANACH SPACES OF CONTINUOUS FUNCTIONS

Glasgow Mathematical Journal ◽

10.1017/s0017089521000100 ◽

2021 ◽

pp. 1-14

Author(s):

R.M. CAUSEY

Keyword(s):

Tensor Product ◽

Banach Spaces ◽

Tensor Products ◽

Continuous Functions ◽

Hausdorff Spaces ◽

Projective Tensor Product ◽

Projective Tensor ◽

Spaces Of Continuous Functions

Abstract Galego and Samuel showed that if K, L are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is c0-saturated if and only if it is subprojective if and only if K and L are both scattered. We remove the hypothesis of metrizability from their result and extend it from the case of the twofold projective tensor product to the general n-fold projective tensor product to show that for any $n\in\mathbb{N}$ and compact, Hausdorff spaces K1, …, K n , $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ is c0-saturated if and only if it is subprojective if and only if each K i is scattered.

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