Embeddings of local fields in simple algebras and simplicial structures
Skodlerack, Daniel (Universität Münster. Mathematisches Institut)

Data:	2014
Resum:	We give a geometric interpretation of Broussous{Grabitz embedding types. We fix a central division algebra D of finite index over a non-Archimedean local field F and a positive integer m. Further we fix a hereditary order a of Mm(D) and an unramified field extension EjF in Mm(D) which is embeddable in D and which normalizes a. Such a pair (E, a) is called an embedding. The embedding types classify the GLm(D)-conjugation classes of these embeddings. Such a type is a class of matrices with non-negative integer entries. We give a formula which allows us to recover the embedding type of (E, a) from the simplicial type of the image of the barycenter of a under the canonical isomorphism, from the set of Ex-fixed points of the reduced building of GLm(D) to the reduced building of the centralizer of Ex in GLm(D). Conversely the formula allows to calculate the simplicial type up to cyclic permutation of the Coxeter diagram.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Embeddings types ; Buildings ; Simple algebras ; Non-archimedean local fields
Publicat a:	Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 499-516, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287188
DOI: 10.5565/PUBLMAT_58214_25

18 p, 418.1 KB

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