Simultaneous direct sum decompositions of several multivariate polynomials
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912265435873280 |
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| author | Fang, Lishan Huang, Hua-Lin Liao, Lili |
| author_facet | Fang, Lishan Huang, Hua-Lin Liao, Lili |
| contents | We consider the problem of simultaneous direct sum decomposition of a set of multivariate polynomials. To this end, we extend Harrison's center theory for a single homogeneous polynomial to this broader setting. It is shown that the center of a set of polynomials is a special Jordan algebra, and simultaneous direct sum decompositions of the given polynomials are in bijection with complete sets of orthogonal idempotents of their center algebra. Several examples are provided to illustrate the performance of this method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous direct sum decompositions of several multivariate polynomials Fang, Lishan Huang, Hua-Lin Liao, Lili Rings and Algebras 15A69, 13P05 We consider the problem of simultaneous direct sum decomposition of a set of multivariate polynomials. To this end, we extend Harrison's center theory for a single homogeneous polynomial to this broader setting. It is shown that the center of a set of polynomials is a special Jordan algebra, and simultaneous direct sum decompositions of the given polynomials are in bijection with complete sets of orthogonal idempotents of their center algebra. Several examples are provided to illustrate the performance of this method. |
| title | Simultaneous direct sum decompositions of several multivariate polynomials |
| topic | Rings and Algebras 15A69, 13P05 |
| url | https://arxiv.org/abs/2503.01205 |