Elementary superalgebras. (English) Zbl 1298.16034
The work deals with some properties of a special class of finite dimensional superalgebras, the elementary superalgebras [see Y. Han and D. Zhao, J. Algebra 321, No. 12, 3668-3680 (2009; Zbl 1223.16018)]. The authors prove that a superalgebra is elementary if and only if its Hochschild extension is elementary. For these algebras they relate the trace of the Coxeter matrix with the dimension of the Hochschild (co)homology. The used techniques are standard.
Reviewer: Alice Fialowski (Davis)
MSC:
16W55 | “Super” (or “skew”) structure |
16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
16E10 | Homological dimension in associative algebras |
16G20 | Representations of quivers and partially ordered sets |
Keywords:
elementary superalgebras; Hochschild cohomology; Hochschild extensions; Coxeter transformationsCitations:
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