Homology of certain algebras defined by graphs |
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Authors: | KH Kim FW Roush |
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Institution: | Mathematics Research Group, Alabama State University, Montgomery, Alabama 36101, U.S.A. |
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Abstract: | Let K(G) for a finite graph G with vertices v1,...,vn denote the K-algebra with generators X1,...,Xn and defining relations XiXj=XjXi if and only if vi is not connected to vj by an edge in G. We describe centralizers of monomials, show that the centralizer of a monomial is again a graph algebra, prove a unique factorization theorem for factorizations of monomials into commuting factors, compute the homology of K(G), and show that K(G) is the homology ring of a certain loop space. We also construct a K(π, 1) explicitly where π is the group with generators X1,...,Xn and defining relations XiXj=XjXi if and only if vi is not connected to vj by an edge in G. |
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