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Top‐stable degenerations of finite‐dimensional representations I
Author(s) -
HuisgenZimmermann Birge
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm031
Subject(s) - partially ordered set , mathematics , context (archaeology) , pure mathematics , representation (politics) , combinatorics , chain (unit) , layering , algebra over a field , physics , paleontology , botany , astronomy , politics , political science , law , biology
Given a finite‐dimensional representation M of a finite‐dimensional algebra, two hierarchies of degenerations of M are analyzed in the context of their natural orders: the poset of those degenerations of M which share the top M / JM with M (here J denotes the radical of the algebra) and the sub‐poset of those which share the full radical layering gl ( J l M / J l +1 M gr ) l ⩾0 with M . In particular, the article addresses the existence of proper top‐stable or layer‐stable degenerations — more generally, it addresses the sizes of the corresponding posets including bounds on the lengths of saturated chains — as well as structure and classification.