Cluster networks and Bruhat-Tits buildings
نویسنده
چکیده
Clustering procedure for the case where instead of a fixed metric one applies a family of metrics is considered. In this case instead of a classification tree one obtains a classification network (a directed acyclic graph with non directed cycles). Relation to Bruhat–Tits buildings is discussed. Dimension of a general cluster system is considered.
منابع مشابه
Bruhat-tits Buildings and Analytic Geometry
This paper provides an overview of the theory of Bruhat-Tits buildings. Besides, we explain how Bruhat-Tits buildings can be realized inside Berkovich spaces. In this way, Berkovich analytic geometry can be used to compactify buildings. We discuss in detail the example of the special linear group. Moreover, we give an intrinsic description of Bruhat-Tits buildings in the framework of non-Archim...
متن کاملCompactification of the Bruhat-Tits building of PGL by lattices of smaller rank
In this paper we construct a compactification of the Bruhat-Tits building associated to the group PGL(V ) by attaching all the Bruhat-Tits buildings of PGL(W ) for non-trivial subspaces W of V as a boundary. MSC (2000): 20E42, 20G25
متن کاملEssays on representations of real groups Symmetric spaces of semi-simple groups
In Cartan’s original proof, the fixed point theorem was about Riemannian spaces of negative curvature, but I’ll use instead a simpler geometric notion due to [Bruhat-Tits:1972]. This allows an argument that is somewhat shorter and more direct than the standard one presented, for example, in [Helgason:1968]. The original application of the criterion of Bruhat-Tits was to buildings, as explained ...
متن کاملKac-Moody groups over ultrametric fields
The Kac-Moody groups studied here are the minimal (=algebraic) and split ones, as introduced by J. Tits in [8]. When they are defined over an ultrametric field, it seems natural to associate to them some analogues of the Bruhat-Tits buildings. Actually I came to this problem when I was trying to build new buildings of nondiscrete type. If G is a Kac-Moody group over an ultrametric field K, I wa...
متن کاملBruhat-tits Theory from Berkovich’s Point of View. Ii. Satake Compactifications of Buildings
In the paper Bruhat-Tits theory from Berkovich’s point of view. I — Realizations and compactifications of buildings, we investigated various realizations of the Bruhat-Tits building B(G,k) of a connected and reductive linear algebraic group G over a non-Archimedean field k in the framework of V. Berkovich’s non-Archimedean analytic geometry. We studied in detail the compactifications of the bui...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1404.6960 شماره
صفحات -
تاریخ انتشار 2014