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

Author(s):  
Paul Bruillard ◽  
Julia Plavnik ◽  
Eric C. Rowell ◽  
Qing Zhang

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.

1983 ◽  
Vol 35 (1) ◽  
pp. 68-100
Author(s):  
Tibor Bisztriczky

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.


Author(s):  
A. Cant ◽  
C. A. Hurst

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.


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

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 294
Author(s):  
Daniel López-Aguayo ◽  
Servando López Aguayo

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.


Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 381 ◽  
Author(s):  
Takayuki Hibi ◽  
Nan Li

Cutting a polytope is a very natural way to produce new classes of interesting polytopes. Moreover, it has been very enlightening to explore which algebraic and combinatorial properties of the original polytope are hereditary to its subpolytopes obtained by a cut. In this work, we devote our attention to all the separating hyperplanes for some given polytope (integral and convex) and study the existence and classification of such hyperplanes. We prove the existence of separating hyperplanes for the order and chain polytopes for any finite posets that are not a single chain, and prove there are no such hyperplanes for any Birkhoff polytopes. Moreover, we give a complete separating hyperplane classification for the unit cube and its subpolytopes obtained by one cut, together with some partial classification results for order and chain polytopes.


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