Quaternionic and octonionic structures of the exceptional lie algebras

Mehmet Koca*

*المؤلف المقابل لهذا العمل

نتاج البحث

1 اقتباس (Scopus)

ملخص

The Cayley-Dickson procedure has been used to construct the root systems of SO(8), SO(9) and the exceptional Lie algebra F4 in terms of quaternions. The Aut(F4) has a simple presentation of the form (O,O) ⊕ (O,O)* where 0 represents the binary octahedral group. Two sets of quaternionic root system of F4, symbolically written [F4, F4] = F4 + e7F4, describe the octonionic root system of E7 where the root system of the exceptional Lie algebra E7 are represented by the imaginary octonions. The automorphism group of the octonionic root system of E7 preserving the octonion algebra is the Chevalley group G2(2) where the maximal subgroups of G2(2) are the automorphism groups of the octonionic root systems of the maximal Lie algebras E6, SU(2) x SO(12) and SU(8) of E7. Another pairing of the quaternionic roots of the form [F 4, F4] = F4 + σF4, constitutes the root system of E8 in terms of icosians where half of the roots describe the roots of the noncrystallographic Coxeter group H4. The relevance of H4 to E8 and the maximal subgroups of H 4 have been discussed. Polyhedral structures obtained from the quaternionic root systems of H4 are described as the orbits of H 3.

اللغة الأصليةEnglish
عنوان منشور المضيفMathematical Physics - Proceedings of the 12th Regional Conference
ناشرWorld Scientific Publishing Co. Pte Ltd
الصفحات25-30
عدد الصفحات6
رقم المعيار الدولي للكتب (المطبوع)9812705910, 9789812705914
المعرِّفات الرقمية للأشياء
حالة النشرPublished - 2007
الحدث12th Regional Conference on Mathematical Physics - Islamabad
المدة: مارس ٢٧ ٢٠٠٦أبريل ١ ٢٠٠٦

سلسلة المنشورات

الاسمMathematical Physics - Proceedings of the 12th Regional Conference

Other

Other12th Regional Conference on Mathematical Physics
الدولة/الإقليمPakistan
المدينةIslamabad
المدة٣/٢٧/٠٦٤/١/٠٦

ASJC Scopus subject areas

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