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Hou, Bo; Yang, Shilin

Elementary superalgebras. (English) Zbl 1298.16034

Algebra Colloq. 19, No. 4, 673-682 (2012).
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 transformations

Citations:

Zbl 1223.16018
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Full Text: DOI

References:

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