Stratified Algebra
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913859271393280 |
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| author | Semenov, Stanislav |
| author_facet | Semenov, Stanislav |
| contents | We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their implications for algebraic dynamics, and present concrete matrix-based models that satisfy different subsets of these axioms. Both associative and bracket-sensitive constructions are considered, with an emphasis on stratum-breaking propagation and permutation symmetry. This framework proposes a paradigm shift in the way algebraic structures are conceived: instead of enforcing uniform global rules, it introduces stratified layers with context-dependent interactions. Such a rethinking of algebraic organization allows for the modeling of systems where local consistency coexists with global asymmetry, non-associativity, and semantic transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stratified Algebra Semenov, Stanislav General Mathematics 17A30, 17A36, 15A75 F.4.1; G.1.0 We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their implications for algebraic dynamics, and present concrete matrix-based models that satisfy different subsets of these axioms. Both associative and bracket-sensitive constructions are considered, with an emphasis on stratum-breaking propagation and permutation symmetry. This framework proposes a paradigm shift in the way algebraic structures are conceived: instead of enforcing uniform global rules, it introduces stratified layers with context-dependent interactions. Such a rethinking of algebraic organization allows for the modeling of systems where local consistency coexists with global asymmetry, non-associativity, and semantic transitions. |
| title | Stratified Algebra |
| topic | General Mathematics 17A30, 17A36, 15A75 F.4.1; G.1.0 |
| url | https://arxiv.org/abs/2505.18863 |