Abstract
Let Λ be a finite-dimensional superalgebra over a field K. A characterization of an elementary superalgebra Λ is given by a quiver and a weight function. It is shown that Λ is elementary if and only if its Hochschild extension is elementary. Furthermore, if Λ is elementary of finite global dimension and {e1, …, en} is a complete set of gr-primitive orthogonal idempotents of Λ, then the following equalities hold: [Formula: see text] where ΦΛ is the Coxeter matrix of Λ, tr is the trace function of a matrix, HHi(Λ) and HHi(Λ) are the i-th Hochschild homology and cohomology, respectively.
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