Inverse of Frobenius Graphs and Flexibility

  • 투고 : 2004.05.07
  • 발행 : 2005.12.23

초록

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.

키워드

참고문헌

  1. J. Algebra v.287 no.1 On Weak Crossed Products, Frobenius Algebras and Weak Bruhat Ordering Aljouiee, A.
  2. Lobachevskii Journal of Mathematics v.14 On the Brauer Monoid of S3 Aljouiee, A.
  3. J. Algebra v.174 On Crossed Product Algebras Arising from Weak Cocycles Haile, D.
  4. J. Algebra v.91 The Brauer Monoid of a Field Haile, D.
  5. Amer. J. Math. v.105 Almost Invertible Cohomology Theory and the Classification of Idempotent Cohomology Classes and Algebras by Partially Ordered Sets with a Galois Group Action Haile, D.;Larson, R.;Sweedler, M.
  6. Communications in Algebra v.19 no.1 Weak Galois Cohomology and Group Extension Stimets, R.