2,549 research outputs found

    Coincidence site modules in 3-space

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    The coincidence site lattice (CSL) problem and its generalization to Z-modules in Euclidean 3-space is revisited, and various results and conjectures are proved in a unified way, by using maximal orders in quaternion algebras of class number 1 over real algebraic number fields.Comment: 25 page

    Annales Mathematicae et Informaticae (42.)

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    Piecewise principal comodule algebras

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    A comodule algebra P over a Hopf algebra H with bijective antipode is called principal if the coaction of H is Galois and P is H-equivariantly projective (faithfully flat) over the coaction-invariant subalgebra PcoH. We prove that principality is a piecewise property: given N comodule-algebra surjections P → P_i whose kernels intersect to zero, P is principal if and only if all P_i’s are principal. Furthermore, assuming the principality of P, we show that the lattice these kernels generate is distributive if and only if so is the lattice obtained by intersection with PcoH. Finally, assuming the above distributivity property, we obtain a flabby sheaf of principal comodule algebras over a certain space that is universal for all such N-families of surjections P → P_i and such that the comodule algebra of global sections is P
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