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Embedding orders into central simple algebras

Benjamin Linowitz, Thomas R. Shemanske (2012)

Journal de Théorie des Nombres de Bordeaux

The question of embedding fields into central simple algebras B over a number field K was the realm of class field theory. The subject of embedding orders contained in the ring of integers of maximal subfields L of such an algebra into orders in that algebra is more nuanced. The first such result along those lines is an elegant result of Chevalley [6] which says that with B = M n ( K ) the ratio of the number of isomorphism classes of maximal orders in B into which the ring of integers of L can be embedded...

Embeddings of maximal tori in orthogonal groups

Eva Bayer-Fluckiger (2014)

Annales de l’institut Fourier

We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic 2 to contain a maximal torus of a given type.

Endomorphism algebras of motives attached to elliptic modular forms

Alexander F. Brown, Eknath P. Ghate (2003)

Annales de l’institut Fourier

We study the endomorphism algebra of the motive attached to a non-CM elliptic modular cusp form. We prove that this algebra has a sub-algebra isomorphic to a certain crossed product algebra X . The Tate conjecture predicts that X is the full endomorphism algebra of the motive. We also investigate the Brauer class of X . For example we show that if the nebentypus is real and p is a prime that does not divide the level, then the local behaviour of X at a place lying above p is essentially determined...

Endomorphismes d’algèbres de suites

Ahmed Ait-Mokhtar, Abdelkader Necer, Alain Salinier (2008)

Journal de Théorie des Nombres de Bordeaux

Cet article traite des endomorphismes de l’algèbre de Hadamard des suites et plus particulièrement de l’algèbre des suites récurrentes linéaires. Il caractérise les endomorphismes continus de l’algèbre des suites et contient, dans le cas d’un corps commutatif de caractéristique nulle, une détermination complète des endomorphismes continus de l’algèbre des suites récurrentes linéaires grâce à la notion nouvelle d’application semi-affine de dans .

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