Ta'lim innovatsiyasi va integratsiyasi

sl ALGEBRANING ANTI-ROTA-BAKSTER OPERATORLARI

Azizov Majidxon Ergashxon o‘g‘li.

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Abstract

Rota-Bakster operatorlari dastlab Jan-Karlo Rota va Richard Baksterlarning
ishlariga foydalanilgan bo‘lib, hozirgi kunda matematikaning bir qator sohalariga
tarqalib bormoqda. Ushbu operatorlar avvalllari kombinatorika va ehtimollar
nazariyasida ko‘plab foydalanilgan bo‘lsa, so‘nggi paytlarda algebrada ham keng
qo‘llanilmoqda.
Glen Bakster, 1960-yilda Rota-Bakster operatorlari yordamida ehtimollik
taqsimotlariga oid ma’lum bir xususiyatni qanoatlantiruvchi quyidagi maxsus Bakster
tenglamasini kiritdi [3]:

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References

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C. Bai, A unified algebraic approach to the classical Yang-Baxter equation. J.

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G. Baxter, An analytic problem whose solution follows from a simple algebraic

identity. Pacific J. Math, 10(3), (1960) 731-742.

G. Liu, C. Bai, Anti-pre-Lie algebras, Novikov algebras and commutative 2-

cocycles on Lie algebras. Journal of Algebra, 609, (2022) 337-379.