The universal cover of an algebra without double bypass

The universal cover of an algebra without double bypass

Let A be a basic and connected finite dimensional algebra over a field k of characteristic zero. We show that if the quiver of A has no double bypass then the fundamental group (as defined in [17]) of any presentation of A by quiver and relations is the quotient of the fundamental group of a privileged presentation of A. Then we show that the Galois covering of A associated with this privileged...

The universal cover of a monomial triangular algebra without multiple arrows

Let A be a basic connected finite dimensional algebra over an algebraically closed field k. Assuming that A is monomial and that the ordinary quiver Q of A has no oriented cycle and no multiple arrows, we prove that A admits a universal cover with group the fundamental group of the underlying space of Q.

An Overview of Modern Universal Algebra

This article, aimed specifically at young mathematical logicians, gives a gentle introduction to some of the central achievements and problems of universal algebra during the last 25 years. I intend in this article to introduce nonspecialists to the fact that there are deep results in contemporary universal algebra. The first four sections give the context in which universal algebra has somethi...

The Universal Lie algebra

The Kontsevich integral of a knot K lies in an algebra of diagrams Ac(S ). This algebra is (up to completion) a symmetric algebra of a graded module P , where P is the set of primitive elements of Ac(S ). The elements of P are represented by S-diagrams K such that the complement of the circle in K is connected and non empty. On the other hand there is an isomorphism from ⊕Bn to Ac(S ), where Bn...

Universal Algebra