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Elliptic root systems of type $A_1$, a combinatorial study | ||
| Transactions on Combinatorics | ||
| مقاله 2، دوره 8، شماره 4، اسفند 2019، صفحه 11-21 اصل مقاله (264.74 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2019.117338.1648 | ||
| نویسنده | ||
| Zahra Kharaghani* | ||
| Department of mathematics, University of Isfahan, Isfahan, Iran | ||
| چکیده | ||
| We consider some combinatorics of elliptic root systems of type $A_1$. In particular, with respect to a fixed reflectable base, we give a precise description of the positive roots in terms of a ``positivity'' theorem. Also the set of reduced words of the corresponding Weyl group is precisely described. These then lead to a new characterization of the core of the corresponding Lie algebra, namely we show that the core is generated by positive root spaces. | ||
| کلیدواژهها | ||
| Elliptic root systems؛ Elliptic Lie algebras؛ Jordan algebras | ||
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آمار تعداد مشاهده مقاله: 604 تعداد دریافت فایل اصل مقاله: 492 |
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