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Proceedings of the London Mathematical Society Advance Access originally published online on September 20, 2007
Proceedings of the London Mathematical Society 2008 96(1):163-198; doi:10.1112/plms/pdm031
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© 2007 London Mathematical Society

Top-stable degenerations of finite-dimensional representations I

Birge Huisgen-Zimmermann

Department of Mathematics
University of California
Santa Barbara, CA 93106
USA

Received 31 August 2005. Revision received 3 April 2007.

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(JlM/Jl+1Mgr)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.

2000 Mathematics Subject Classification 16G10, 16G20, 16D70, 14D06, 14D20.

Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday

This research was partially supported by a grant fromthe National Science Foundation.


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