Pluckerians twisted with linear forms and Druzkowski maps
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911582949212160 |
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| author | Chen, Li |
| author_facet | Chen, Li |
| contents | We introduce a class of so-called Pl$\ddot{\mathrm{u}}$cker polynomials with respect to $2l\times l$ matrices, which varies the standard quadratic Pl$\ddot{\mathrm{u}}$cker expression by increased power and twisted linear forms. Besides general interests exhibited by novel algebraic identities and delicate nested structures, these polynomials fit into Dru$\dot{z}$kowski's well-known reduction of the Jacobian Conjecture. The core jacobian condition therein breaks into homogeneous linear equations with polynomial coefficients, and the Pl$\ddot{\mathrm{u}}$cker polynomials are applied to study both existence and expression of their nontrivial solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pluckerians twisted with linear forms and Druzkowski maps Chen, Li Number Theory Functional Analysis We introduce a class of so-called Pl$\ddot{\mathrm{u}}$cker polynomials with respect to $2l\times l$ matrices, which varies the standard quadratic Pl$\ddot{\mathrm{u}}$cker expression by increased power and twisted linear forms. Besides general interests exhibited by novel algebraic identities and delicate nested structures, these polynomials fit into Dru$\dot{z}$kowski's well-known reduction of the Jacobian Conjecture. The core jacobian condition therein breaks into homogeneous linear equations with polynomial coefficients, and the Pl$\ddot{\mathrm{u}}$cker polynomials are applied to study both existence and expression of their nontrivial solutions. |
| title | Pluckerians twisted with linear forms and Druzkowski maps |
| topic | Number Theory Functional Analysis |
| url | https://arxiv.org/abs/2407.07911 |