Cocycles and Bilenear Forms

  IJMTT-book-cover
 
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

MLA

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.

Abstract
— 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.

References


[1]. K.J. Horadom & W. De Launey, Cocyclic Development of Designs, Journal of Algebraic Combinatorics 2: 267-290, 1993.
[2]. D.L. Flannery, Calculation of Cocyclic Matrices, Journal of Pure & Applied. Algebra: 181-190.,1996.
[3]. K.J. Horadam & A.A.I. Perera, Codes from Cocycles, Lecture notes in Computer Science, Applied Algebra, Algebraic Algorithms and Error Correcting Codes 1255:151-163,1997.

Keywords
                 Cocycle matrix, bilinear forms.