• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.561-570
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• 2005

Weak Crossed Product Algebras correspond to certain graphs called lower subtractive graphs. The properties of such algebras can be obtained by studying this kind of graphs ([4], [5]). In [1], the author showed that a weak crossed product is Frobenius and its restricted subalgebra is symmetric if and only if its associated graph has a unique maximal vertex. A special construction of these graphs came naturally and was known as standard lower subtractive graph. It was a deep question that when such a special graph possesses unique maximal vertex? This work is to answer the question partially and to give a particular characterization for such graphs at which the corresponding algebras are isomorphic. A graph that follows the mentioned characterization is called flexible. Flexibility is to some extend a generalization of the so-called Coxeter groups and its weak Bruhat ordering.