Cocycles and Bilenear Forms

International Journal of Mathematical Trends and Technology (IJMTT)          
© 2011 by IJMTT Journal
Volume-2 Issue-2                           
Year of Publication : 2011
Authors : A.A.I Perera, D.G.T.K. Samarasiri


A.A.I Perera, D.G.T.K. Samarasiri"Cocycles and Bilenear Forms"International Journal of Mathematical Trends and Technology (IJMTT),V2(2):15-19.June 2011. Published by Seventh Sense Research Group.

— A ( two dimensional ) cocycle  is a mapping  such that g h k G g h gh k g hk h k  where G is a finite group and C is a finite abelian group. Additive form of the cocycle equation is g, h g  h, k g, h  k h, k  g, h,k G A cocycle naturally displays as a matrix, g h G M g h , and this matrix is the Hadamard product of Inflation, Transgression and Coboundary matrices. In our work, we prove that the bilinear form is a cocycle and the converse is not true by giving a counter example.


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                 Cocycle matrix, bilinear forms.