О дифференцированиях в групповых алгебрах и других алгебраических структурах

Обложка
  • Авторы: Арутюнов А.А.1,2
  • Учреждения:
    1. ФГБУН «Институт проблем управления им. В.А. Трапезникова» Российской академии наук
    2. ФГАОУ ВО «Московский физико-технический институт (национальный исследовательский университет)»
  • Выпуск: Том 27, № 140 (2022)
  • Страницы: 305-317
  • Раздел: Научные статьи
  • URL: https://journals.rcsi.science/2686-9667/article/view/296486
  • ID: 296486

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Аннотация

Работа посвящена обзору известных результатов, связанных с исследованиями дифференцирований в групповых алгебрах, бимодулях и других алгебраических структурах, а также различным обобщениям и вариациям данной задачи. Дается обзор результатов, посвященных дифференцированиям в алгебрах L1(G); в алгебрах фон Ноймана и в банаховых бимодулях. Обсуждаются алгебраические задачи, в частности дифференцирования в группах, (σ,τ)-дифференцирования и исчисление Фокса. Также дается обзор некоторых результатов, связанных с приложением к псевдодифференциальным операторам и построению символьного исчисления. В заключении описываются некоторые результаты, связанные с описанием дифференцирований, как характеров на группоиде присоединенного действия. Описаны также некоторые приложения: к теории кодирования, теории концов метрических пространств и грубой геометрии.

Об авторах

Андроник Арамович Арутюнов

ФГБУН «Институт проблем управления им. В.А. Трапезникова» Российской академии наук; ФГАОУ ВО «Московский физико-технический институт (национальный исследовательский университет)»

Автор, ответственный за переписку.
Email: andronick.arutyunov@gmail.com
ORCID iD: 0000-0002-6878-0993

кандидат физико-математических наук, старший научный сотрудник; доцент кафедры высшей математики

Россия, 117997, Российская Федерация, г. Москва, ул. Профсоюзная, 65; 141701, Российская Федерация, Московская обл., г. Долгопрудный, Институтский переулок, 9

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