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A POLYNOMIAL APPROACH TO COCYCLES OVER ELEMENTARY ABELIAN GROUPS

Part of: Connections with homological algebra and category theory Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  01 October 2008

D. G. FARMER  and
K. J. HORADAM
D. G. FARMER
Affiliation:
RMIT University, Melbourne, VIC 3001, Australia (email: David.Farmer@ems.rmit.edu.au)
K. J. HORADAM*
Affiliation:
RMIT University, Melbourne, VIC 3001, Australia (email: Kathy.Horadam@rmit.edu.au)
*
✉For correspondence; e-mail: Kathy.Horadam@rmit.edu.au
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Abstract

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We derive bivariate polynomial formulae for cocycles and coboundaries in Z2(ℤpn,ℤpn), and a basis for the (pn−1−n)-dimensional GF(pn)-space of coboundaries. When p=2 we determine a basis for the -dimensional GF(2n)-space of cocycles and show that each cocycle has a unique decomposition as a direct sum of a coboundary and a multiplicative cocycle of restricted form.

Keywords

2-cocyclecoboundarymultiplicative cocyclebasisPascal’s triangle

MSC classification

Secondary: 11T06: Polynomials 20J06: Cohomology of groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 2 , October 2008 , pp. 177 - 190
Copyright
Copyright © 2008 Australian Mathematical Society

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