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 HH 2 (A) in the sense of Sköldberg.2010 Mathematics Subject Classification. 16E40, 16G20, 16L60.

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Let A be a truncated quiver algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of A is zero in A. We give the number of the indecomposable direct summands of the middle term of an almost split sequence for a class of Hochschild extension algebras of A by the standard duality module D(A).

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