التمثيل المصفوفي لجبر لي المحلول القابل للتفكيك سداسي الأبعاد

القسم: Article

إصدار

مجلد 35 عدد 1 (2026): المجلد 35 العدد 1

منشور

Jan 1, 2026

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1-7

الملخص

تُوسّع هذه الورقة تصنيف اللوب الطوبولوجية المتصلة ثلاثية الأبعاد ، حيث تكون مجموعة الضرب فيها عبارة عن زمرة لي سداسية الأبعاد قابلة للتحلل والحل. بناءً على النتائج المهمة الواردة في [1]، والتي أثبتت انعدام القوى المركزية من الدرجة الثانية لهذه الوب، نستنتج وبشكل صريح تمثيلات مصفوفيه لجبر لي المرتبط بها. تُعد هذه التمثيلات بالغة الأهمية لإكمال التصنيف، إذ تُسهّل التحقق من التوافق مع الشروط العملية المعرفة على جبر لي. نحدد 26 عائلة مميزة من زمر لي المصفوفية، بما في ذلك 18 مجموعة تتميز بأحادية المركز و8 مجموعات ثنائية المركز. بالإضافة إلى ذلك، نُوضح التوافق بين هذه المجموعات وجبر لي المُشتق منها. تُعالج نتائجنا فجوة قائمة في الأدبيات من خلال توفير إطار منهجي لدراسة العلاقات المتبادلة بين الوب الطوبولوجية وزمر لي المُناظرة لها.

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