scholarly journals CONVEXLY ORDERABLE GROUPS AND VALUED FIELDS

2014 ◽  
Vol 79 (01) ◽  
pp. 154-170
Author(s):  
JOSEPH FLENNER ◽  
VINCENT GUINGONA
Keyword(s):  
Abelian Groups ◽  
Complete Classification ◽  
Necessary Condition ◽  
Valued Fields ◽  
Ordered Groups ◽  
Algebraic Theories ◽  
Convexly Orderable

Abstract We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality are equivalent, and use this to give a complete classification of VC-minimal theories of ordered groups and abelian groups. Consequences for fields are also considered, including a necessary condition for a theory of valued fields to be quasi-VC-minimal. For example, the p-adics are not quasi-VC-minimal.

Groups Admitting only Finitely Many Nilpotent Ring Structures

1986 ◽  
Vol 29 (2) ◽  
pp. 197-203
Author(s):  
Shalom Feigelstock
Keyword(s):  
Abelian Groups ◽  
Complete Classification ◽  
Actual Number ◽  
Nilpotent Ring ◽  
Ring Structures ◽  
Free Case ◽  
Torsion Free

AbstractThe abelian groups which are the additive groups of only finitely many non-isomorphic (associative) nilpotent rings are studied. Progress is made toward a complete classification of these groups. In the torsion free case, the actual number of non-isomorphic nilpotent rings these groups support is obtained.

scholarly journals Sub-prime radical classes determined by zerorings

1975 ◽  
Vol 12 (1) ◽  
pp. 95-97 ◽  
Author(s):  
B.J. Gardner
Keyword(s):  
Abelian Groups ◽  
Complete Classification ◽  
Prime Radical ◽  
Radical Class

It is shown that the correspondence which associates with each radical class τ of abelian groups the (radical) class of prime radical rings with additive groups in τ gives a complete classification of those radical classes of rings which are determined (as lower radicals) by zerorings.

On independent permutation separability criteria

2006 ◽  
Vol 6 (3) ◽  
pp. 277-288
Author(s):  
L. Clarisse ◽  
P. Wocjan
Keyword(s):  
Complete Classification ◽  
Necessary Condition ◽  
Numerical Verification ◽  
Separability Criteria

Recently, P.\ Wocjan and M.\ Horodecki [Open Syst.\ Inf.\ Dyn.\ 12, 331 (2005)] gave a characterization of combinatorially independent permutation separability criteria. Combinatorial independence is a necessary condition for permutations to yield truly independent criteria meaning that no criterion is strictly stronger that any other. In this paper we observe that some of these criteria are still dependent and analyze why these dependencies occur. To remove them we introduce an improved necessary condition and give a complete classification of the remaining permutations. We conjecture that the remaining class of criteria only contains truly independent permutation separability criteria. Our conjecture is based on the proof that for two, three and four parties all these criteria are truly independent and on numerical verification of their independence for up to 8 parties. It was commonly believed that for three parties there were 9 independent criteria, here we prove that there are exactly 6 independent criteria for three parties and 22 for four parties.

Unstable K1-group and homotopy type of certain gauge groups

2006 ◽  
Vol 136 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Hiroaki Hamanaka ◽  
Akira Kono
Keyword(s):  
Gauge Group ◽  
Homotopy Type ◽  
Complete Classification ◽  
Necessary Condition ◽  
Gauge Groups ◽  
Homotopy Types

We denote the group of homotopy set [X, U(n)] by the unstable K1-group of X. In this paper, using the unstable K1-group of the multi-suspended CP2, we give a necessary condition for two principal SU(n)-bundles over §4 to have the associated gauge group of the same homotopy type, which is an improvement of the result of Sutherland and, particularly, show the complete classification of homotopy types of SU(3)-gauge groups over S4.

Inequalities in Discrete Subgroups of PSL(2, R)

1988 ◽  
Vol 40 (1) ◽  
pp. 115-130 ◽  
Author(s):  
Jane Gilman
Keyword(s):  
Discrete Group ◽  
Sufficient Conditions ◽  
Complete Classification ◽  
Necessary Condition ◽  
Discrete Subgroups ◽  
Elementary Subgroup ◽  
Van Vleck ◽  
Necessary And Sufficient ◽  
Number Of Authors

Conditions for a subgroup, F, of PSL(2, R) to be discrete have been investigated by a number of authors. Jørgensen's inequality [5] gives an elegant necessary condition for discreteness for subgroups of PSL(2, C). Purzitsky, Rosenberger, Matelski, Knapp, and Van Vleck, among others [12, 13, 14, 9, 16, 17, 18, 19, 20, 7, 21] studied two generator discrete subgroups of PSL(2, R) in a long series of papers. The complete classification of two generator subgroups was surprisingly complicated and elusive. The most complete result appears in [20].In this paper we use the results of [20] to prove that a nonelementary subgroup F of PSL(2, R) is discrete if and only if every non-elementary subgroup, G, generated by two hyperbolics is discrete (Theorem 5.2) and that F contains no elliptics if and only if each such G is free (Theorem 5.1). Thus, we produce necessary and sufficient conditions for a non-elementary subgroup F of PSL(2, R) to be a discrete group without elliptic elements (Theorem 6.1) or a discrete group containing only hyperbolic elements (Theorem 7.1).

Orderings in locally compact Abelian groups and the theorem of F. and M. Riesz

1983 ◽  
Vol 93 (3) ◽  
pp. 441-457 ◽  
Author(s):  
Edwin Hewitt ◽  
Shozo Koshi
Keyword(s):  
Harmonic Analysis ◽  
Abelian Groups ◽  
Complete Classification ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups

Background (1·1). Ordered Abelian groups have been studied for nearly a century. Since the early 1950's, it has been recognized that orderings in locally compact Abelian groups can play an important rôle in harmonic analysis on such groups. In this paper we study orderings, especially in topological Abelian groups with either topological or measure-theoretic properties, obtaining nearly a complete classification of such orderings. We then apply these results to determine the limitations of the celebrated theorem of F. and M. Riesz on such groups.

scholarly journals A criterion for discrete branching laws for Klein four symmetric pairs and its application to E6(−14)

2020 ◽  
Vol 31 (06) ◽  
pp. 2050049
Author(s):  
Haian He
Keyword(s):  
Lie Group ◽  
Simple Formula ◽  
Complete Classification ◽  
Necessary Condition ◽  
Symmetric Pair ◽  
Branching Laws ◽  
Nonidentity Element

Let [Formula: see text] be a noncompact connected simple Lie group, and [Formula: see text] a Klein four-symmetric pair. In this paper, we show a necessary condition for the discrete decomposability of unitarizable simple [Formula: see text]-modules for Klein for symmetric pairs. Precisely, if certain conditions hold for [Formula: see text], there does not exist a unitarizable simple [Formula: see text]-module that is discretely decomposable as a [Formula: see text]-module. As an application, for [Formula: see text], we obtain a complete classification of Klein four symmetric pairs [Formula: see text], with [Formula: see text] noncompact, such that there exists at least one nontrivial unitarizable simple [Formula: see text]-module that is discretely decomposable as a [Formula: see text]-module and is also discretely decomposable as a [Formula: see text]-module for some nonidentity element [Formula: see text].

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1077
Author(s):  
Yarema A. Prykarpatskyy
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Structure ◽  
Necessary Condition ◽  
Type Representation ◽  
Infinite Hierarchy ◽  
Polynomial Coefficients ◽  
Kdv Type Equations ◽  
Special Case

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

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