5 research outputs found
The cohomological reduction method for computing n-dimensional cocyclic matrices
Provided that a cohomological model for is known, we describe a method
for constructing a basis for -cocycles over , from which the whole set of
-dimensional -cocyclic matrices over may be straightforwardly
calculated. Focusing in the case (which is of special interest, e.g. for
looking for cocyclic Hadamard matrices), this method provides a basis for
2-cocycles in such a way that representative -cocycles are calculated all at
once, so that there is no need to distinguish between inflation and
transgression 2-cocycles (as it has traditionally been the case until now).
When , this method provides an uniform way of looking for higher
dimensional -cocyclic Hadamard matrices for the first time. We illustrate
the method with some examples, for . In particular, we give some
examples of improper 3-dimensional -cocyclic Hadamard matrices.Comment: 17 pages, 0 figure