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Bipartite Graphs Whose Edge Algebras Are Complete Intersections

✍ Scribed by Mordechai Katzman

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 115 KB
Volume: 220
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7919

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✦ Synopsis

Let R be a monomial subalgebra of k x 1

x N generated by square free monomials of degree two. This paper addresses the following question: when is R a complete intersection? For such a k-algebra we can associate a graph G whose vertices are x 1

x N and whose edges are x i x j x i x j ∈ R . Conversely, for any graph G with vertices x 1

x N we define the edge algebra associated with G as the subalgebra of k x 1

x N generated by the monomials x i x j x i x j is an edge of G We denote this monomial algebra by k G . This paper describes all bipartite graphs whose edge algebras are complete intersections.

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