The Hochschild Cohomology Ring of a One Point Extension

Abstract

This paper studies the ring structure of the Hochschild cohomology ring of an algebra. The first main result gives a ring homomorphism from the Hochschild cohomology ring of an algebra A to the Ext-algebra of an A-module. Then, for a one point extension B of a finite dimensional algebra A, we relate the ring structures of the Hochschild cohomology rings of A and B thus giving a method of constructing algebras with non-trivial ring structure on the Hochschild cohomology ring.

Key Words:

• Hochschild cohomology
• One-point extension
• Ext algebra

2000 Mathematics Subject classification:

• Primary 16W50
• Secondary 16G20

Acknowledgments

The first author was partially supported by grants from the National Science Foundation and National Security Agency. The second author was partially funded by a research scholarship from CNPq-Brazil. The third author wishes to thank the University of Leicester for its support in granting study leave, the London Mathematical Society for a Scheme 4 grant, and VPI&SU for its hospitality.