Automorphisms of Incidence Algebras

Abstract

We study automorphisms of the incidence algebra of a finite quasiordered set M. In particular, we describe explicitly the group of outer automorphisms and give a criterion for any automorphism of this algebra to be a product of an inner one and an automorphism of M, which corrects some results of Spiegel (2001).

Key Words:

• Automorphism
• Cohomology
• Incidence algebra
• Partially orderd set
• Simplicial complex

2000 Mathematics Subject Classification:

• Primary 16W20
• Secondary 16S50, 15A30, 06A11

Notes

¹Such incidence algebras coincide with minimal algebras in the sense of Drozd and Kirichenko (1970, Exercise 3.8).

Communicated by D. Happel.