Constructing Irreducible Representations of Finitely Presented Algebras

Constructing Irreducible Representations of Finitely Presented Algebras

We describe an algorithmic test, using the “standard polynomial identity” (and elementary computational commutative algebra), for determining whether or not a finitely presented associative algebra has an irreducible n-dimensional representation. When ndimensional irreducible representations do exist, our proposed procedure can (in principle) produce explicit constructions.

Constructing Matrix Representations of Finitely Presented Groups

The Todd-Coxeter coset enumeration algorithm is one of the most powerful tools of computational group theory. It may be viewed as a means of constructing permutation representations of nitely presented groups. In this paper we present an analogous algorithm for directly constructing matrix representations over many elds. In fact the algorithm is more general than this, and can be used to constr...

Analysing Finitely Presented Groups by Constructing Representations

One idea how to prove that a finitely presented group G is infinite is to construct suitable homomorphisms into infinite matrix groups. In [HoP 92] this is done by starting with a finite image H of G and solving linear equations to check whether the epimorphism onto H can be lifted to a representation whose image is an extension of a ZZ-lattice by H, thus exhibiting an infinite abelian section ...

Finitely Presented Heyting Algebras

In this paper we study the structure of finitely presented Heyting algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every such Heyting algebra is in fact coHeyting, improving on a result of Ghilardi who showed that Heyting algebras free on a finite set of generators are co-Heyting. Along the way we give a new and simple proof of the finite model pro...

Irreducible Representations of Operator Algebras