Cocycles and Bilenear Forms

A.A.I Perera; D.G.T.K. Samarasiri

doi:https://doi.org/10.14445/22315373/IJMTT-V2I2P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 2 | Issue 2 | Year 2011 | Article Id. IJMTT-V2I2P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V2I2P504

Cocycles and Bilenear Forms

A.A.I Perera, D.G.T.K. Samarasiri

Citation :

A.A.I Perera, D.G.T.K. Samarasiri, "Cocycles and Bilenear Forms," International Journal of Mathematics Trends and Technology (IJMTT), vol. 2, no. 2, pp. 15-17, 2011. Crossref, https://doi.org/10.14445/22315373/IJMTT-V2I2P504

Abstract

A ( two dimensional ) cocycle  is a mapping  : G  G  C 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.

Keywords

Cocycle matrix, bilinear forms.

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.