Vol. 3 No. 1 (2025), Articles
Vol. 3 No. 1 (2025)

FILIFORM 3-LI ALGEBRALARDA YECHILUVCHAN KENGAYTMALARNING O‘LCHAM BO‘YICHA MODELLANISHI

Articles
Published 2025-06-28
Beshimova Shaxnoza
Buxoro Davlat universiteti
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Keywords

3-Li algebra, Filiform algebra, yechiluvchan kengaytma, Nilpotent algebra, Gomologiya nazariyasi, deformatsiya, algebraik modellashtirish, kengaytmalarni klassifikatsiya qilish, ko‘p o‘zgaruvchili ko‘paytma.

Abstract

Ushbu maqolada filiform 3-Li algebralarning strukturalari, ularning klassifikatsiyasi hamda yechiluvchan kengaytmalarning o‘lcham bo‘yicha modellanishi masalalari o‘rganiladi. 3-Li algebralar klassik Lie algebralarning umumlashmasi bo‘lib, uch elementli antikommutativ ko‘paytma va Filippov identiteti orqali aniqlanadi. Filiform 3-Li algebralar esa nilpotent 3-Li algebralarning alohida turi bo‘lib, ularning nilpotentlik darajasi maksimal bo‘ladi va ular struktura jihatidan oddiy, ammo chuqur algebraik xossalarga ega. Yechiluvchan kengaytmalar 3-Li algebralarni yangi o‘lchamdagi algebralarga umumlashtirish imkonini beradi. Bunday kengaytmalarni klassifikatsiya qilishda gomologik yondashuvlar, ayniqsa ikkinchi gomologik guruhlar muhim ahamiyatga ega. Maqolada kengaytmalarni o‘lcham (ya’ni, bazis elementlar soni) ortishi bilan qanday tarzda modellashtirish mumkinligi ko‘rsatiladi. Shu maqsadda differensial komplekslar, deformatsiyalar nazariyasi va ko‘rsatkichli funksiyalardan foydalaniladi.

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