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Geometric and combinatorial structure of a class of spherical folding tessellations – I

Catarina P. Avelino, Altino F. Santos (2017)

Czechoslovak Mathematical Journal

A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tessellations of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle. Within two possible cases of adjacency, only one will be addressed....

Graded morphisms of G -modules

Hanspeter Kraft, Claudio Procesi (1987)

Annales de l'institut Fourier

Let A be finite dimensional C -algebra which is a complete intersection, i.e. A = C [ X 1 , ... , X n ] / ( f 1 , ... , f n ) whith a regular sequences f 1 , ... , f n . Steve Halperin conjectured that the connected component of the automorphism group of such an algebra A is solvable. We prove this in case A is in addition graded and generated by elements of degree 1.

Graphs having no quantum symmetry

Teodor Banica, Julien Bichon, Gaëtan Chenevier (2007)

Annales de l’institut Fourier

We consider circulant graphs having p vertices, with p prime. To any such graph we associate a certain number k , that we call type of the graph. We prove that for p ≫ k the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.

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