Partial classification of modules for the algebra of skew-derivations over the d-dimensional torus

2016 ◽  
Vol 57 (10) ◽  
pp. 101702 ◽  
Author(s):  
Chengkang Xu
Keyword(s):  
Dimensional Torus ◽  
Partial Classification

scholarly journals Partial classification of modules for Lie-algebra of diffeomorphisms of d-dimensional torus

2004 ◽  
Vol 45 (8) ◽  
pp. 3322-3333 ◽  
Author(s):  
S. Eswara Rao
Keyword(s):  
Lie Algebra ◽  
Dimensional Torus ◽  
Partial Classification

C-Nodal Surfaces of Order Three

1983 ◽  
Vol 35 (1) ◽  
pp. 68-100
Author(s):  
Tibor Bisztriczky
Keyword(s):  
Nineteenth Century ◽  
Singular Point ◽  
Algebraic Surface ◽  
Partial Classification ◽  
Differentiability Condition ◽  
Nodal Surfaces

The problem of describing a surface of order three can be said to originate in the mid-nineteenth century when A. Cayley discovered that a non-ruled cubic (algebraic surface of order three) may contain up to twenty-seven lines. Besides a classification of cubics, not much progress was made on the problem until A. Marchaud introduced his theory of synthetic surfaces of order three in [9]. While his theory resulted in a partial classification of a now larger class of surfaces, it was too general to permit a global description. In [1], we added a differentiability condition to Marchaud's definition. This resulted in a partial classification and description of surfaces of order three with exactly one singular point in [2]-[5]. In the present paper, we examine C-nodal surfaces and thus complete this survey.

scholarly journals The algebraic structure of relativistic wave equations

1978 ◽  
Vol 20 (4) ◽  
pp. 446-486 ◽  
Author(s):  
A. Cant ◽  
C. A. Hurst
Keyword(s):  
Lie Algebras ◽  
Algebraic Structure ◽  
Mass Spectra ◽  
Wave Equations ◽  
Relativistic Wave Equations ◽  
Relativistic Wave ◽  
Partial Classification ◽  
The Family ◽  
Image Position

The algebraic structure of relativistic wave equations of the formis considered. This leads to the problem of finding all Lie algebrasLwhich contain the Lorentz Lie algebraso(3, 1) and also contain a “four-vector” αμa such anLgives rise to a family of wave equations. The simplest possibility is the Bhabha equations whereL≅so(5). Some authors have claimed that this is theonlyone, but it is shown that there are many other possibilities still in accord with physical requirements. Known facts about representations, along with Dynkin's theory of the embeddings of Lie algebras, are used to obtain a partial classification of wave equations. The discrete transformationsC, P, Tare also discussed, along with reality properties. Finally, a simple example of a family of wave equations based onL=sp(12) is considered in detail. Theso(3, 1) content and mass spectra are given for the low order members of the family, and the problem of causality is briefly discussed.

scholarly journals Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms

2008 ◽  
Vol 23 (2) ◽  
pp. 137-162 ◽  
Author(s):  
M.J. Parker ◽  
I.N. Stewart ◽  
M.G.M. Gomes
Keyword(s):  
Partial Classification

scholarly journals Antiautomorphisms and Biantiautomorphisms of Some Finite Abelian Groups

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 294
Author(s):  
Daniel López-Aguayo ◽  
Servando López Aguayo
Keyword(s):  
Lower Bound ◽  
Abelian Groups ◽  
Additive Group ◽  
Exact Formula ◽  
Finite Abelian Groups ◽  
Cyclic Groups ◽  
Partial Classification ◽  
Open Questions ◽  
Odd Order

We extend the concepts of antimorphism and antiautomorphism of the additive group of integers modulo n, given by Gaitanas Konstantinos, to abelian groups. We give a lower bound for the number of antiautomorphisms of cyclic groups of odd order and give an exact formula for the number of linear antiautomorphisms of cyclic groups of odd order. Finally, we give a partial classification of the finite abelian groups which admit antiautomorphisms and state some open questions.

scholarly journals On classification of super-modular categories of rank 8

2020 ◽  
pp. 2140017
Author(s):  
Paul Bruillard ◽  
Julia Plavnik ◽  
Eric C. Rowell ◽  
Qing Zhang
Keyword(s):  
Lower Rank ◽  
Partial Classification

We develop categorical and number-theoretical tools for the classification of super-modular categories. We apply these tools to obtain a partial classification of super-modular categories of rank [Formula: see text]. In particular we find three distinct families of prime categories in rank [Formula: see text] in contrast to the lower rank cases for which there is only one such family.

scholarly journals Partial classification of cuspidal simple modules for Virasoro-like algebra

2016 ◽  
Vol 464 ◽  
pp. 266-278 ◽  
Author(s):  
Jian-Jian Jiang ◽  
Wei-Qiang Lin
Keyword(s):  
Simple Modules ◽  
Partial Classification

scholarly journals On periodic mapping data of a two-dimensional torus with one saddle orbit

2019 ◽  
Vol 21 (2) ◽  
pp. 164-174
Author(s):  
Anna A. Bosova ◽  
Olga V. Pochinka
Keyword(s):  
Periodic Orbit ◽  
Nodal Point ◽  
Zeta Functions ◽  
Topological Classification ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Periodic Surface ◽  
Periodic Data ◽  
Surface Diffeomorphism

Periodic data of diffeomorphisms with regular dynamics on surfaces were studied using zeta functions in a series of already classical works by such authors as P. Blanchard, J. Franks, S. Narasimhan, S. Batterson and others. The description of periodic data for gradient-like diffeomorphisms of surfaces were given in the work of A. Bezdenezhnykh and V. Grines by means of the classification of periodic surface transformations obtained by J. Nielsen. V. Grines, O. Pochinka, S. Van Strien showed that the topological classification of arbitrary Morse-Smale diffeomorphisms on surfaces is based on the problem of calculating periodic data of diffeomorphisms with a single saddle periodic orbit. Namely, the construction of filtering for Morse-Smale diffeomorphisms makes it possible to reduce the problem of studying periodic surface diffeomorphism data to the problem of calculating periodic diffeomorphism data with a single saddle periodic orbit. T. Medvedev, E. Nozdrinova, O. Pochinka solved this problem in a general formulation, that is, the periods of source orbits are calculated from a known period of the sink and saddle orbits. However, these formulas do not allow to determine the feasibility of the obtained periodic data on the surface of this kind. In an exhaustive way, the realizability problem is solved only on a sphere. In this paper we establish a complete list of periodic data of diffeomorphisms of a two-dimensional torus with one saddle orbit, provided that at least one nodal point of the map is fixed.

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