1. Fine decompositions of algebraic systems induced by bases.
- Author
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Calderón Martín, Antonio J. and Gaye, Babacar
- Subjects
- *
POISSON algebras , *VECTOR spaces , *ORBITS (Astronomy) , *SUPERALGEBRAS , *ALGEBRA - Abstract
We consider algebraic systems with several products, including unary products, S (as examples we can take linear spaces, algebras, superalgebras, hom-algebras, triple systems, hom-triple systems, Poisson algebras, Bol algebras, n-algebras, etc.) We show that any basis of S gives rise to a decomposition of S as a direct sum of indecomposable well-described ideals (fine decomposition). The simplicity of the components in this decomposition is also characterized. There are as many non-isomorphic fine decompositions as orbits in a determined action. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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