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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2015
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1506.01502 |
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| _version_ | 1866913521330028544 |
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| author | Hu, Ya-Qing Huang, Hua-Lin Zhang, Chi |
| author_facet | Hu, Ya-Qing Huang, Hua-Lin Zhang, Chi |
| contents | We introduce a series of $\Z_2^n$-graded quasialgebras $\bbP_n(m)$ which generalizes Clifford algebras, higher octonions, and higher Cayley algebras. The constructed series of algebras and their minor perturbations are applied to contribute explicit solutions to the Hurwitz problem on compositions of quadratic forms. In particular, we provide explicit expressions of the well-known Hurwitz-Radon square identities in a uniform way, recover the Yuzvinsky-Lam-Smith formulas, confirm the third family of admissible triples proposed by Yuzvinsky in 1984, improve the two infinite families of solutions obtained recently by Lenzhen, Morier-Genoud and Ovsienko, and construct several new infinite families of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1506_01502 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | $\Z_2^n$-graded quasialgebras and the Hurwitz problem on compositions of quadratic forms Hu, Ya-Qing Huang, Hua-Lin Zhang, Chi Quantum Algebra Number Theory Rings and Algebras 16S35, 16W50, 11E25 We introduce a series of $\Z_2^n$-graded quasialgebras $\bbP_n(m)$ which generalizes Clifford algebras, higher octonions, and higher Cayley algebras. The constructed series of algebras and their minor perturbations are applied to contribute explicit solutions to the Hurwitz problem on compositions of quadratic forms. In particular, we provide explicit expressions of the well-known Hurwitz-Radon square identities in a uniform way, recover the Yuzvinsky-Lam-Smith formulas, confirm the third family of admissible triples proposed by Yuzvinsky in 1984, improve the two infinite families of solutions obtained recently by Lenzhen, Morier-Genoud and Ovsienko, and construct several new infinite families of solutions. |
| title | $\Z_2^n$-graded quasialgebras and the Hurwitz problem on compositions of quadratic forms |
| topic | Quantum Algebra Number Theory Rings and Algebras 16S35, 16W50, 11E25 |
| url | https://arxiv.org/abs/1506.01502 |