Normal forms for algebras of connections

Normal forms for algebras of connection

Recent years have seen a growing interest towards algebraic structures that are able to express formalisms di.erent from the standard, tree-like presentation of terms. Many of these approaches reveal a speci1c interest towards the application to the ‘distributed and concurrent systems’ 1eld, but an exhaustive comparison between them is sometimes di4cult, because their presentations can be quite...

Generic Algebras: Rational Parametrization and Normal Forms

For every algebraically closed field k of characteristic different from 2, we prove the following: (1) Generic finite dimensional (not necessarily associative) kalgebras of a fixed dimension, considered up to isomorphism, are parametrized by the values of a tuple of algebraically independent over k rational functions in the structure constants. (2) There exists an “algebraic normal form”, to wh...

Normal Forms for Representations of Representation-finite Algebras

Normal Forms for Operators via Gröbner Bases in Tensor Algebras

We propose a general algorithmic approach to noncommutative operator algebras generated by linear operators using quotients of tensor algebras. In order to work with reduction systems in tensor algebras, Bergman’s setting provides a tensor analog of Gröbner bases. We discuss a modification of Bergman’s setting that allows for smaller reduction systems and tends to make computations more efficie...

Orbital Normal Forms for a family of-zero Singularity

Consider a Dynamical system x'=F(x,µ) such that its linear part has a pair of imaginary eigenvalues and one zero eigenvalue (Hopf zero singularity). Recently, the simplest normal form for this singular system has been obtained by sl(2) Lie algebra theory and the decomposition of space into three invariant subspaces. The normal form of this singular system is divided into three general cases. In...