Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Peter Abramenko"'
Autor:
Hendrik Van Maldeghem, Peter Abramenko
Publikováno v:
Indagationes Mathematicae. 15:305-319
Let Δ and Δ′ be two buildings of the same type (W, S), viewed as sets of chambers endowed with“distance” functions δ and δ′, respectively, admitting values in the common Weyl group W, which is a Coxeter group with standard generating set
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ee70fc747c5c22882cc20b446cbd7c5b
https://doi.org/10.1016/s0019-3577(04)80001-6
https://doi.org/10.1016/s0019-3577(04)80001-6
Publikováno v:
JOURNAL OF ALGEBRA
In this paper we define generalised spheres in buildings using the simplicial structure and Weyl distance in the building, and we derive an explicit formula for the cardinality of these spheres. We prove a generalised notion of distance regularity in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8e6a0a24269b6c0a5dd8b486c4dae937
Autor:
Hendrik Van Maldeghem, Peter Abramenko
Publikováno v:
Journal of Geometry. 74:7-28
In this paper, we characterize the natural opposition relation on the set of flags of a generalized polygon. We also investigate when a certain relation on any rank 2 geometry of finite diameter is equivalent to the opposition relation in a generaliz
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::06ac6d40fd3ebd2b23bd64f21a003fa2
https://doi.org/10.1007/pl00012539
https://doi.org/10.1007/pl00012539
Autor:
Peter Abramenko, Gabriele Nebe
Publikováno v:
Mathematische Annalen. 322:537-562
A concrete lattice chain model for the buildings of the classical groups over non archimedean complete skew fields is given. The building axioms are proved in a uniform way using hereditary orders with involution instead of lattice chains.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ce41cf107750e26a5900a82a5326d152
https://doi.org/10.1007/s002080200004
https://doi.org/10.1007/s002080200004
Autor:
Hendrik Van Maldeghem, Peter Abramenko
Publikováno v:
Mathematische Zeitschrift. 238:187-203
In this paper, we characterize twinnings of buildings by 1-twinnings and one further condition concerning twin apartments. Specialized to the spherical case, we obtain new characterizations of the opposition relation in such buildings. We also give a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b085a830d03aee3f981b9aa57db335e6
https://doi.org/10.1007/pl00004899
https://doi.org/10.1007/pl00004899
Autor:
H. Van Maldeghem, Peter Abramenko
Publikováno v:
Annals of Combinatorics. 4:125-137
In this paper, we prove a combinatorial property of twin apartments and opposition of chambers in twin buildings. We then characterize adjacency of chambers in twin buildings by meansof opposition of chambers. As an application, we study maps which s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::366f34194a3307576c36d75e86bbf4f3
https://doi.org/10.1007/s000260050001
https://doi.org/10.1007/s000260050001
Autor:
Peter Abramenko, Hendrik Van Maldeghem
Publikováno v:
European Journal of Combinatorics. 20(6):461-468
We show that the geometry of the elements opposite a certain flag in a Moufang polygon is always connected, up to some small cases. This completes the determination of all Moufang polygons for which this geometry is disconnected.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9b7445e3884a3ce68945e0863436fe4c
Autor:
Peter Abramenko, Mark A. Ronan
Publikováno v:
Geometriae Dedicata. 73:1-9
A twin building is a pair of buildings along with a certain ’codistance' between chambers of one building, and chambers of the other. All spherical buildings can be regarded as twin buildings (such a building is twinned with itself in a natural way
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e031237d5023e2c1d78ac38b58c4ddf9
https://doi.org/10.1023/a:1005065400830
https://doi.org/10.1023/a:1005065400830
Autor:
Bernhard Mühlherr, Peter Abramenko
Publikováno v:
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics. 325:701-706
Resume On donne une presentation de certaines BN -paires jumelees comme sommes amalgamees. Notre resultat generalise un theoreme de Tits sur les BN -paires spheriques. En utilisant la theorie des immeubles jumeles, les auteurs ont obtenu le resultat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::17d008ccedbf091f382fb985188e1181
https://doi.org/10.1016/s0764-4442(97)80044-4
https://doi.org/10.1016/s0764-4442(97)80044-4
Autor:
Peter Abramenko
Publikováno v:
Israel Journal of Mathematics. 87:203-223
LetG be a simple Chevalley group of rankn and Γ=G( $$Fq[t]$$ ). Then the finiteness length of Γ shall be determined by studying the action of Γ on the Bruhat-Tits buildingX ofG $$(F_q ((\frac{1}{t})))$$ . This is always possible provided that cert
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::04e56f6c0c18c58703924fc8b5ace194
https://doi.org/10.1007/bf02772995
https://doi.org/10.1007/bf02772995