A CLASS OF EXCEPTIONAL BERNSTEIN ALGEBRAS ASSOCIATED TO GRAPHS

Given a simple graph G without loops and a field F of characteristic n ot 2 we construct an exceptional Bernstein algebra F(G) over F and sho w that F(G) is indecomposable if and only if G is connected. The dupli cate of F(G) is a Bernstein Jordan algebra whose type is determined by the number of points and lines of G. We comment briefly how to extend the theory to the case of multigraphs.