The hierarchies of identities and closed products for multiple complexes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912943470280704 |
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| author | Levin, Daniel Zuevsky, Alexander |
| author_facet | Levin, Daniel Zuevsky, Alexander |
| contents | We consider infinite $\Z_\Z$-index complexes $\mathcal C$ of spaces with elements depending on a number of parameters, complete with respect to a linear associative regular inseparable multilinear product. The existence of nets of vanishing ideals of orders of and powers of differentials is assumed for subspaces of $\mathcal C$-spaces. In the polynomial case of orders and powers of the differentials, we derive the hierarchies of differential identities and closed multiple products. We prove that a set of maximal orders and powers for differentials, differential conditions, together with coherence conditions on indices of a complex $\mathcal C$ elements generate families of multi-graded differential algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16271 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The hierarchies of identities and closed products for multiple complexes Levin, Daniel Zuevsky, Alexander Functional Analysis We consider infinite $\Z_\Z$-index complexes $\mathcal C$ of spaces with elements depending on a number of parameters, complete with respect to a linear associative regular inseparable multilinear product. The existence of nets of vanishing ideals of orders of and powers of differentials is assumed for subspaces of $\mathcal C$-spaces. In the polynomial case of orders and powers of the differentials, we derive the hierarchies of differential identities and closed multiple products. We prove that a set of maximal orders and powers for differentials, differential conditions, together with coherence conditions on indices of a complex $\mathcal C$ elements generate families of multi-graded differential algebras. |
| title | The hierarchies of identities and closed products for multiple complexes |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2405.16271 |