Non-semigroup gradings of associative algebras

It is known that there are Lie algebras with non-semigroup gradings, i.e. such that the binary operation on the grading set is not associative. We provide a similar example in the class of associative algebras.

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Bibliographic Details
Published in:Linear algebra and its applications 2017-06, Vol.523, p.52-58
Main Author: Zusmanovich, Pasha
Format: Article
Language:English
Subjects:
Algebra
Binary system
Group theory
Lie groups
Linear algebra
Matrix
Non-semigroup grading
δ-Derivation
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Description
Summary:It is known that there are Lie algebras with non-semigroup gradings, i.e. such that the binary operation on the grading set is not associative. We provide a similar example in the class of associative algebras.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2017.01.038