Purely Atomic Representations of Higher-Rank Graph $$\varvec{C}^{\varvec{*}}$$C∗-Algebras
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DOI: 10.1007/s00020-018-2493-z
Abstract: We study purely atomic representations of $$C^*$$C∗-algebras associated to row-finite and source-free higher-rank graphs. We describe when purely atomic representations are unitarily equivalent and we give necessary and sufficient conditions for a purely atomic representation… read more here.
Keywords: atomic representations; representations higher; varvec; higher rank ... See more keywords
First order rigidity of non-uniform higher rank arithmetic groups
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DOI: 10.1007/s00222-019-00866-5
Abstract: If $$\Gamma $$Γ is an irreducible non-uniform higher-rank characteristic zero arithmetic lattice (for example $${{\,\mathrm{SL}\,}}_n({\mathbb {Z}})$$SLn(Z), $$n \ge 3$$n≥3) and $$\Lambda $$Λ is a finitely generated group that is elementarily equivalent to $$\Gamma $$Γ, then… read more here.
Keywords: higher rank; uniform higher; first order; order rigidity ... See more keywords
Higher rank hyperbolicity
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DOI: 10.1007/s00222-020-00955-w
Abstract: The large-scale geometry of hyperbolic metric spaces exhibits many distinctive features, such as the stability of quasi-geodesics (the Morse Lemma), the visibility property, and the homeomorphism between visual boundaries induced by a quasi-isometry. We prove… read more here.
Keywords: rank hyperbolicity; geometry; higher rank; rank ... See more keywords
Explicit strong boundedness for higher rank symplectic groups
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DOI: 10.1016/j.jalgebra.2022.03.041
Abstract: Abstract. This paper gives an explicit argument to show strong boundedness for Sp 2n (R) for R a ring of S-algebraic integers or a semi-local ring. This gives a quantitative version of the abstract result… read more here.
Keywords: higher rank; boundedness; rank symplectic; strong boundedness ... See more keywords
KMS states on the Toeplitz algebras of higher-rank graphs
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DOI: 10.1016/j.jmaa.2020.123841
Abstract: Abstract The Toeplitz algebra T C ⁎ ( Λ ) for a finite k-graph Λ is equipped with a continuous one-parameter group α r for each r ∈ R k , obtained by composing the… read more here.
Keywords: kms states; higher rank; states toeplitz; rank graphs ... See more keywords
Elliptical higher rank numerical range of some Toeplitz matrices
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DOI: 10.1016/j.laa.2018.03.024
Abstract: Abstract The higher rank numerical range is described for a class of matrices which happen to be unitarily reducible to direct sums of (at most) 2-by-2 blocks. In particular, conditions are established under which tridiagonal… read more here.
Keywords: rank numerical; rank; higher rank; numerical range ... See more keywords
Local rigidity of higher rank non-abelian action on torus
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DOI: 10.1017/etds.2017.77
Abstract: In this paper, we show local smooth rigidity for higher rank ergodic nilpotent action by toral automorphisms. In former papers all examples for actions enjoying the local smooth rigidity phenomenon are higher rank and have… read more here.
Keywords: rigidity higher; higher rank; smooth rigidity; rigidity ... See more keywords
Higher rank rigidity for Berwald spaces
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DOI: 10.1017/etds.2018.130
Abstract: We generalize the higher rank rigidity theorem to a class of Finsler spaces, i.e. Berwald spaces. More precisely, we prove that a complete connected Berwald space of finite volume and bounded non-positive flag curvature with… read more here.
Keywords: berwald spaces; rigidity berwald; higher rank; rank rigidity ... See more keywords
Applying early divergent characters in higher rank taxonomy of Melampsorineae (Basidiomycota, Pucciniales)
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DOI: 10.1080/21501203.2022.2089262
Abstract: ABSTRACT Rust fungi in the order Pucciniales represent one of the largest groups of phytopathogens, which occur on mosses, ferns to advanced monocots and dicots. Seven suborders and 18 families have been reported so far,… read more here.
Keywords: higher rank; rank taxonomy; melampsorineae; early divergent ... See more keywords
On the Theory of Higher Rank Euler, Kolyvagin and Stark Systems
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DOI: 10.1093/imrn/rnz103
Abstract: Mazur and Rubin have recently developed a theory of higher rank Kolyvagin and Stark systems over principal artinian rings and discrete valuation rings. We describe a natural extension of (a slightly modified version of) their… read more here.
Keywords: theory higher; kolyvagin stark; higher rank; rank ... See more keywords
Local Eigenvalue Statistics for Higher-Rank Anderson Models After Dietlein-Elgart
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DOI: 10.1142/s0129055x23500174
Abstract: We use the method of eigenvalue level spacing developed by Dietlein and Elgart (arXiv:1712.03925) to prove that the local eigenvalue statistics (LES) for the Anderson model on $Z^d$, with uniform higher-rank $m \geq 2$, single-site… read more here.
Keywords: higher rank; dietlein elgart; eigenvalue statistics; local eigenvalue ... See more keywords