The 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants for SL(3,C) x SL(3,C) x SL(3,C)
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arXiv
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| Format: | Preprint |
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2013
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| _version_ | 1866908594594643968 |
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| author | Bremner, Murray Hu, Jiaxiong Oeding, Luke |
| author_facet | Bremner, Murray Hu, Jiaxiong Oeding, Luke |
| contents | We briefly review previous work on the invariant theory of 3 x 3 x 3 arrays. We then recall how to generate arrays of arbitrary size m_1 x ... x m_k with hyperdeterminant 0. Our main result is an explicit formula for the 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants of degrees 6, 9 and 12 for the action of the Lie group SL(3,C) x SL(3,C) x SL(3,C). We apply our calculations to Nurmiev's classification of normal forms for 3 x 3 x 3 arrays. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1310_3257 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | The 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants for SL(3,C) x SL(3,C) x SL(3,C) Bremner, Murray Hu, Jiaxiong Oeding, Luke Algebraic Geometry Symbolic Computation Representation Theory Primary 13A50, Secondary 15A72, 17B10 We briefly review previous work on the invariant theory of 3 x 3 x 3 arrays. We then recall how to generate arrays of arbitrary size m_1 x ... x m_k with hyperdeterminant 0. Our main result is an explicit formula for the 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants of degrees 6, 9 and 12 for the action of the Lie group SL(3,C) x SL(3,C) x SL(3,C). We apply our calculations to Nurmiev's classification of normal forms for 3 x 3 x 3 arrays. |
| title | The 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants for SL(3,C) x SL(3,C) x SL(3,C) |
| topic | Algebraic Geometry Symbolic Computation Representation Theory Primary 13A50, Secondary 15A72, 17B10 |
| url | https://arxiv.org/abs/1310.3257 |