The ordinary quivers of Hochschild extension algebras for self-injective Nakayama algebras

ABSTRACT

Let T be a Hochschild extension algebra of a finite dimensional algebra A over a field K by the standard duality A-bimodule Hom_K(A, K). In this paper, we determine the ordinary quiver of T if A is a self-injective Nakayama algebra by means of the ℕ-graded second Hochschild homology group HH₂(A) in the sense of Sköldberg.

KEYWORDS:

• Hochschild extension
• Hochschild (co)homology
• trivial extension
• self-injective Nakayama algebra
• symmetric algebra
• quiver

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16E40
• 16G20
• 16L60

Acknowledgments

The authors thank Professor Takahiko Furuya for many valuable comments and suggestions. The authors would also like to express their gratitude to the referees for valuable comments and helpful suggestions towards the improvement of the article.