The Adjacency Matrix of Directed Graphs over the Grassmann Algebra
by
Péter Körtesi
University of Miskolc

The main aim of this short talk is to give a concise and transparent reformulation of Swan's grapg theoretical theorem (which is equivalent to the classical Amitsur-Levitski theorem on the minimal PI of matrix algebras. Labelling the edges of a directed graph by the anticommutative generators of a Grassmann algebra, we define its adjacency matrix in a usual way. We prove that this matrix is nilpotent of index 2n , where n denotes the number of vertices. The proof is based on Rosset's approach to the Amitsur-Levitski theorem.

Date received: November 12, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabw-18.