. R T ] 1 4 M ay 2 00 2 GENERALIZED ASSOCIAHEDRA VIA QUIVER REPRESENTATIONS
نویسنده
چکیده
We provide a quiver-theoretic interpretation of certain smooth complete simplicial fans associated to arbitrary finite root systems in recent work of S. Fomin and A. Zelevinsky. The main properties of these fans then become easy consequences of the known facts about tilting modules due to K. Bongartz, D. Happel and C. M. Ringel.
منابع مشابه
0 M ay 2 00 6 BGP - reflection functors and cluster combinatorics ∗
We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the ”truncated simple reflections” on the set of almost positive roots Φ≥−1 associated to a finite dimensional semisimple Lie algebra. Combining with the tilting theory in cluster categories developed in [4], we ...
متن کاملGeneralized Associahedra via Quiver Representations
We provide a quiver-theoretic interpretation of certain smooth complete simplicial fans associated to arbitrary finite root systems in recent work of S. Fomin and A. Zelevinsky. The main properties of these fans then become easy consequences of the known facts about tilting modules due to K. Bongartz, D. Happel and C. M. Ringel.
متن کاملBgp-reflection Functors and Cluster Combinatorics
We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the ”truncated simple reflections” on the set of almost positive roots Φ≥−1 associated to a finite dimensional semisimple Lie algebra. Combining with the tilting theory in cluster categories developed in [4], we ...
متن کاملar X iv : m at h / 06 09 18 4 v 2 [ m at h . C O ] 1 8 M ay 2 00 7 FACES OF GENERALIZED PERMUTOHEDRA
The aim of the paper is to calculate face numbers of simple generalized permutohedra, and study their f -, hand γ-vectors. These polytopes include permutohedra, associahedra, graph-associahedra, simple graphic zonotopes, nestohedra, and other interesting polytopes. We give several explicit formulas for h-vectors and γ-vectors involving descent statistics. This includes a combinatorial interpret...
متن کاملar X iv : m at h / 05 05 08 2 v 1 [ m at h . R A ] 5 M ay 2 00 5 FINITE - DIMENSIONAL ALGEBRAS AND QUIVERS
This is an overview article on finite-dimensional algebras and quivers, written for the Encyclopedia of Mathematical Physics. We cover path algebras, Ringel-Hall algebras and the quiver varieties of Lusztig and Nakajima.
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:
دوره شماره
صفحات -
تاریخ انتشار 2008