Certain partitions on a set and their applications to different classes of graded algebras

Certain partitions on a set and their applications to different classes of graded algebras

Let (𝔘, ɛu) and (𝔅, ɛb) be two pointed sets. Given a family of three maps ℱ = {f1 : 𝔘 → 𝔘; f2 : 𝔘 × 𝔘 → 𝔘; f3 : 𝔘 × 𝔘 → 𝔅}, this family provides an adequate decomposition of 𝔘 \ {ɛu} as the orthogonal disjoint union of well-described ℱ-invariant subsets. This decomposition is applied to the structur...

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Bibliographic Details
Main Authors: Calderón Martín Antonio J., Dieme Boubacar
Format: Article
Language:English
Published: Sciendo 2021-06-01
Series:Communications in Mathematics
Subjects:
set
application
graded algebra
involutive algebra
quadratic algebra
weak h*-algebra
structure theory
03e75
17a01
16w50
08a05
17a45
Online Access:https://doi.org/10.2478/cm-2021-0021
Description
Summary:Let (𝔘, ɛu) and (𝔅, ɛb) be two pointed sets. Given a family of three maps ℱ = {f1 : 𝔘 → 𝔘; f2 : 𝔘 × 𝔘 → 𝔘; f3 : 𝔘 × 𝔘 → 𝔅}, this family provides an adequate decomposition of 𝔘 \ {ɛu} as the orthogonal disjoint union of well-described ℱ-invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak H*-algebras.
ISSN:2336-1298

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