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Relevant bibliographies by topics / Lattice quotients

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Journal articles

Academic literature on the topic 'Lattice quotients'

Author: Grafiati

Published: 25 May 2024

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Journal articles on the topic "Lattice quotients"

1

Mühle, Henri. "Noncrossing Arc Diagrams, Tamari Lattices, and Parabolic Quotients of the Symmetric Group." Annals of Combinatorics 25, no. 2 (2021): 307–44. http://dx.doi.org/10.1007/s00026-021-00532-9.

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AbstractOrdering permutations by containment of inversion sets yields a fascinating partial order on the symmetric group: the weak order. This partial order is, among other things, a semidistributive lattice. As a consequence, every permutation has a canonical representation as a join of other permutations. Combinatorially, these canonical join representations can be modeled in terms of arc diagrams. Moreover, these arc diagrams also serve as a model to understand quotient lattices of the weak order. A particularly well-behaved quotient lattice of the weak order is the well-known Tamari lattic

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2

Dubsky, Brendan. "Incidence Category of the Young Lattice, Injections Between Finite Sets, and Koszulity." Algebra Colloquium 28, no. 02 (2021): 195–212. http://dx.doi.org/10.1142/s1005386721000171.

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We study the quadratic quotients of the incidence category of the Young lattice defined by the zero relations corresponding to adding two boxes to the same row, or to the same column, or both. We show that the last quotient corresponds to the Koszul dual of the original incidence category, while the first two quotients are, in a natural way, Koszul duals of each other and hence they are in particular Koszul self-dual. Both of these two quotients are known to be basic representatives in the Morita equivalence class of the category of injections between finite sets. We also present a new, rather

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3

Thumbakara, Rajesh K. "On Intuitionistic Fuzzy Filters of Intuitionistic Fuzzy Coframes." Journal of Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/793824.

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Frame theory is the study of topology based on its open set lattice, and it was studied extensively by various authors. In this paper, we study quotients of intuitionistic fuzzy filters of an intuitionistic fuzzy coframe. The quotients of intuitionistic fuzzy filters are shown to be filters of the given intuitionistic fuzzy coframe. It is shown that the collection of all intuitionistic fuzzy filters of a coframe and the collection of all intutionistic fuzzy quotient filters of an intuitionistic fuzzy filter are coframes.

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4

Alvarado-García, Alejandro, César Cejudo-Castilla, Hugo Alberto Rincón-Mejía, and Ivan Fernando Vilchis-Montalvo. "Pseudocomplements and strong pseudocomplements in lattices of module classes." Journal of Algebra and Its Applications 17, no. 01 (2018): 1850016. http://dx.doi.org/10.1142/s0219498818500160.

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In this work, we consider the existence and construction of pseudocomplements in some lattices of module classes. The classes of modules belonging to these lattices are defined via closure under operations such as taking submodules, quotients, extensions, injective hulls, direct sums or products. We characterize the rings for which the lattices [Formula: see text]-tors (of hereditary torsion classes), [Formula: see text]-nat (the lattice of natural classes) and [Formula: see text]-conat (the lattice of conatural classes) coincide.

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5

Wójtowicz, Marek. "The lattice-isometric copies ofℓ∞(Γ)in quotients of Banach lattices". International Journal of Mathematics and Mathematical Sciences 2003, № 47 (2003): 3003–6. http://dx.doi.org/10.1155/s0161171203210528.

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LetEbe a Banach lattice and letMbe a norm-closed and Dedekindσ-complete ideal ofE. IfEcontains a lattice-isometric copy ofℓ∞, thenE/Mcontains such a copy as well, orMcontains a lattice copy ofℓ∞. This is one of the consequences of more general results presented in this paper.

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6

Pilaud, Vincent. "Brick polytopes, lattice quotients, and Hopf algebras." Journal of Combinatorial Theory, Series A 155 (April 2018): 418–57. http://dx.doi.org/10.1016/j.jcta.2017.11.014.

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7

Ma, Jingjing, and R. H. Redfield. "Fields of quotients of lattice-ordered domains." algebra universalis 52, no. 4 (2005): 383–401. http://dx.doi.org/10.1007/s00012-004-1875-z.

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8

Demonet, Laurent, Osamu Iyama, Nathan Reading, Idun Reiten та Hugh Thomas. "Lattice theory of torsion classes: Beyond 𝜏-tilting theory". Transactions of the American Mathematical Society, Series B 10, № 18 (2023): 542–612. http://dx.doi.org/10.1090/btran/100.

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The aim of this paper is to establish a lattice theoretical framework to study the partially ordered set t o r s A \mathsf {tors} A of torsion classes over a finite-dimensional algebra A A . We show that t o r s A \mathsf {tors} A is a complete lattice which enjoys very strong properties, as bialgebraicity and complete semidistributivity. Thus its Hasse quiver carries the important part of its structure, and we introduce the brick labelling of its Hasse quiver and use it to study lattice congruences of t o r s A \mathsf {tors} A . In particular, we give a representation-theoretical interpretat

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9

KAKARIADIS, EVGENIOS T. A. "Finite-dimensional approximations for Nica–Pimsner algebras." Ergodic Theory and Dynamical Systems 40, no. 12 (2019): 3375–402. http://dx.doi.org/10.1017/etds.2019.44.

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We give necessary and sufficient conditions for nuclearity of Cuntz–Nica–Pimsner algebras for a variety of quasi-lattice ordered groups. First we deal with the free abelian lattice case. We use this as a stepping-stone to tackle product systems over quasi-lattices that are controlled by the free abelian lattice and satisfy a minimality property. Our setting accommodates examples like the Baumslag–Solitar lattice for $n=m>0$ and the right-angled Artin groups. More generally, the class of quasi-lattices for which our results apply is closed under taking semi-direct and graph products. In the

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10

Jenča, G., and S. Pulmannová. "Ideals and quotients in lattice ordered effect algebras." Soft Computing 5, no. 5 (2001): 376–80. http://dx.doi.org/10.1007/s005000100139.

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