ar X iv : 0 71 2 . 18 04 v 1 [ m at h . A C ] 1 1 D ec 2 00 7 SIMPLICIAL COMPLEXES AND MACAULAY ’ S INVERSE SYSTEMS
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چکیده
Let ∆ be a simplicial complex on V an n), where each ai ≥ 2. By utilizing the technique of Macaulay's inverse systems, we can explicitly describe the socle of A in terms of ∆. As a consequence, we determine the simplicial complexes, that we will call levelable, for which there exists a tuple (a1,. .. , an) such that A(∆, a1,. .. , an) is a level algebra.
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