arXiv subjects
Publications and source records attributed to Edward Green.
We return to the fusion rules for the Drinfeld double of the duals of the generalised Taft algebras that we studied in [9]. We first correct some proofs and statements in [9] that were incorrect, using stable homomorphisms. We then complete this with new results on fusion rules for the modules we had not studied in [9] and a classification of endotrivial and algebraic modules.
If $f$ is an idempotent in a ring $Λ$, then we find sufficient \linebreak conditions which imply that the cohomology rings $\oplus_{n\ge 0}Ext^n_Λ(Λ/{\br},Λ/{\br})$ and \linebreak $\oplus_{n\ge 0}Ext^n_{fΛf}(fΛf/f{\br} f,fΛf/f{\br} f)$ are eventually isomorphic. This result allows us to compare finite generation and GK dimension of the cohomology rings $Λ$ and $fΛf$. We are also able to compare the global dimensions of $Λ$ and $fΛf$.
We present a mathematical model: dynamical systems over finite sets (DSF), and we show that Boolean and discrete genetic models are special cases of DFS. In this paper, we prove that a function defined over finite sets with different number of elements can be represented as a polynomial function over a finite field. Given the data of a function defined over different finite sets, we describe an algorithm to obtain all the polynomial functions associated to this data. As a consequence, all the functions defined in a regulatory network can be represented as a polynomial function in one variable or in several variables over a finite field. We apply these results to study the reverse engineering problem.