LI ALGEBRALARINING LOKAL VA 2-LOKAL ANTI- DIFFERENSIALLASLARI
Keywords:
Kalit so‘zlar: Lie algebrasi, anti-differensiallash, lokal anti-differensiallash, 2- lokal anti-differensiallash, oddiy algebra, yarim oddiy algebra, ichki anti- differensiallash, differensiallash, Jacobi tengligi, sl(n,F).Abstract
ANNOTATSIYA
Ushbu maqolada chekli o‘lchamli Lie algebralarida lokal va 2-lokal anti-
differensiallashlar nazariyasi keng ko‘lamda o‘rganiladi. Lokal va 2-lokal anti-
differensiallash tushunchalarining aniq ta'riflari beriladi, ular o‘rtasidagi farq va
umumiy xossalar tahlil qilinadi. Asosiy natija sifatida — char(F) = 0 bo‘lgan F maydon
ustidagi chekli o‘lchamli oddiy Lie algebrasida har bir lokal anti-differensiallash
haqiqiy anti-differensiallash ekanligi isbotlanadi. Shuningdek, 2-lokal anti-
differensiallashlar uchun analogik teorema o‘rganiladi va yarim oddiy Lie
algebralariga umumlashtiriladi. Klassik Lie algebralarining — sl(n,F), so(n,F),
sp(2n,F) — anti-differensiallashlar algebrasining tuzilishi tavsiflanadi. Barcha ichki
anti-differensiallashlar anti-derivatsion sifatida tasniflanadi va Lie algebrasining
markaziy kengaytmalari bilan aloqasi muhokama qilinadi. Olingan natijalar mavjud
adabiyotlardagi differensiallashlar nazariyasi bilan qiyosiy tahlil qilinadi hamda
kelajakdagi tadqiqot yo‘nalishlari belgilab beriladi.
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