scholarly journals Generalized string-net model for unitary fusion categories without tetrahedral symmetry

2020 ◽  
Vol 102 (11) ◽  
Author(s):  
Alexander Hahn ◽  
Ramona Wolf
Keyword(s):  
Tetrahedral Symmetry ◽  
Fusion Categories

Coordination state of cobalt(II) ions in solution and on a sulphonated organic polymer

1979 ◽  
Vol 44 (8) ◽  
pp. 2330-2337 ◽  
Author(s):  
Jindřiška Maternová ◽  
Anastas A. Andreev ◽  
Dimitrii M. Shopov ◽  
Karel Setínek
Keyword(s):  
Acetic Acid ◽  
Coordination Sphere ◽  
Glacial Acetic Acid ◽  
Organic Polymer ◽  
Octahedral Complex ◽  
Coordination State ◽  
Tetrahedral Symmetry ◽  
Liquid Acid ◽  
Homogeneous Phase ◽  
Bromide Ion

It was found spectroscopically that cobalt(II) acetate dissolved in glacial acetic acid forms the octahedral complex [Co(OAc)2(HOAc)4] which in the presence of bromide ions gives the octahedral [Co(OAc)Br(HOAc)4] and tetrahedral bromo(acetate)cobalt(II) complexes with the higher number of Br- ions. When attached to an organic polymer cobalt(II) ions are bonded in the form of octahedral [Co(H2O)6]2+ cations which form with acetic acid similar complexes as in homogeneous phase and are able to coordinate one bromide ion. Drying the copolymer possessing octahedral hexaaquocobalt(II) cations leads to tetrahedral aquocomplexes which are solvated by gaseous acetic acid and converted into the acetate complexes with the liquid acid. The latter contain the acid in the inner coordination sphere and have tetrahedral symmetry.

Verfeinerung der Kristallstruktur von Tripalladium-di-tetrathiophospliat Pd3(PS4)2 Refinement of the Crystal Structure of Tripalladium-di-tetrathiophosphate Pda3(PS4)2

1983 ◽  
Vol 38 (4) ◽  
pp. 426-427 ◽  
Author(s):  
Arndt Simon ◽  
Karl Peters ◽  
Harry Hahn
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Title Compound ◽  
Type Structure ◽  
Tetrahedral Symmetry ◽  
X Ray ◽  
X Ray Crystallography ◽  
Planar Environment

Abstract The structure of the title compound has been determined by X-ray crystallography. The title compound is synthesized from the elements at 600 °C. Its crystal structure, derived from powder data [3] is refined by single crystal diffractometer data. The structure is trigonal (P3̅ml, α = 684.1(1), c = 724.4(1) pm); Pd2+ cations and PS43- anions form a network with an anti-Claudetite (AS2O3) type structure. The PS4 units are distinctly distorted from ideal tetrahedral symmetry. The Pd atoms have a planar environment of 4 S atoms.

scholarly journals On Normal Tensor Functors and Coset Decompositions for Fusion Categories

2014 ◽  
Vol 23 (4) ◽  
pp. 591-608 ◽  
Author(s):  
A. Bruguières ◽  
Sebastian Burciu
Keyword(s):  
Fusion Categories ◽  
Normal Tensor

scholarly journals FROM RIBBON CATEGORIES TO GENERALIZED YANG–BAXTER OPERATORS AND LINK INVARIANTS (AFTER KITAEV AND WANG)

2013 ◽  
Vol 24 (01) ◽  
pp. 1250126 ◽  
Author(s):  
SEUNG-MOON HONG
Keyword(s):  
The Other ◽  
Polynomial Invariant ◽  
Link Invariants ◽  
Fusion Categories ◽  
New Family ◽  
Kauffman Polynomial ◽  
Twist Structure

We consider two approaches to isotopy invariants of oriented links: one from ribbon categories and the other from generalized Yang–Baxter (gYB) operators with appropriate enhancements. The gYB-operators we consider are obtained from so-called gYBE objects following a procedure of Kitaev and Wang. We show that the enhancement of these gYB-operators is canonically related to the twist structure in ribbon categories from which the operators are produced. If a gYB-operator is obtained from a ribbon category, it is reasonable to expect that two approaches would result in the same invariant. We prove that indeed the two link invariants are the same after normalizations. As examples, we study a new family of gYB-operators which is obtained from the ribbon fusion categories SO (N)2, where N is an odd integer. These operators are given by 8 × 8 matrices with the parameter N and the link invariants are specializations of the two-variable Kauffman polynomial invariant F.

Ligand Field-Spin Orbit Energy Levels in the d4 and d6 Electron Configurations of Octahedral and Tetrahedral Symmetry

1974 ◽  
Vol 29 (1) ◽  
pp. 31-41 ◽  
Author(s):  
E. König ◽  
S. Kremer
Keyword(s):  
Strong Field ◽  
Energy Levels ◽  
Coulomb Repulsion ◽  
Orbit Interaction ◽  
Complete Agreement ◽  
Ligand Field ◽  
Spin Orbit ◽  
Tetrahedral Symmetry ◽  
Spin Orbit Interaction ◽  
Orbit Perturbation

The complete ligand field -Coulomb repulsion -spin orbit interaction matrices have been derived for the d4 and d6 electron configurations within octahedral (Oh) and tetrahedral (Td) symmetry. The calculations were perform ed in both the weak-field and strong-field coupling schemes and complete agreement of the results was achieved. The energy matrices are parametrically dependent on ligand field (Dq), Coulomb repulsion (B, C) and spin-orbit interaction (ζ). Correct energy diagrams are presentend which display the splittings by spin-orbit perturbation as well as the effect of configuration mixing. Applications to the interpretation of optical spectral data, to the detailed behavior at the crossover of ground terms, and to complete studies in magnetism are pointed out.

scholarly journals The center of the extended Haagerup subfactor has 22 simple objects

2017 ◽  
Vol 28 (01) ◽  
pp. 1750009 ◽  
Author(s):  
Scott Morrison ◽  
Kevin Walker
Keyword(s):  
Fusion Category ◽  
Dimension Function ◽  
Fusion Ring ◽  
Fusion Categories ◽  
Modular Data ◽  
Grothendieck Rings ◽  
Combinatorial Data

We explain a technique for discovering the number of simple objects in [Formula: see text], the center of a fusion category [Formula: see text], as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring [Formula: see text] and the dimension function [Formula: see text]. In particular, we apply this to deduce that the center of the extended Haagerup subfactor has 22 simple objects, along with their decompositions as objects in either of the fusion categories associated to the subfactor. This information has been used subsequently in [T. Gannon and S. Morrison, Modular data for the extended Haagerup subfactor (2016), arXiv:1606.07165 .] to compute the full modular data. This is the published version of arXiv:1404.3955 .

ABOUT SOME ISSUES IN THE TETRON MODEL

2008 ◽  
Vol 23 (33) ◽  
pp. 2835-2845 ◽  
Author(s):  
BODO LAMPE
Keyword(s):  
Elementary Particles ◽  
Tetrahedral Symmetry ◽  
Vector Bosons ◽  
Recent Developments

After a prologue which clarifies some issues left open in my last paper, the main features of the tetron model of elementary particles are discussed in the light of recent developments, in particular the formation of strong and electroweak vector bosons and a microscopic understanding of how the observed tetrahedral symmetry of the fermion spectrum may arise.

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