On locally nilpotent derivations of polynomial algebra in three variables

Мұқаба
  • Авторлар: Dasgupta N.1, Gaifullin S.A.2,3,4
  • Мекемелер:
    1. MURTI Research Center, Gandhi Institute of Technology and Management, Bengaluru, Karnataka, India
    2. Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
    3. Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
    4. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
  • Шығарылым: Том 216, № 4 (2025)
  • Беттер: 3-34
  • Бөлім: Articles
  • URL: https://journals.rcsi.science/0368-8666/article/view/306694
  • DOI: https://doi.org/10.4213/sm10094
  • ID: 306694

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

In this paper we investigate locally nilpotent derivations on the polynomial algebra in three variables over a field of characteristic zero. We introduce an iterating construction giving all locally nilpotent derivations of rank $2$. This construction allows us to obtain examples of non-triangularizable locally nilpotent derivations of rank $2$. We also show that the well-known example of a locally nilpotent derivation of rank $3$, given by Freudenburg, is a member of a large family of new examples of rank $3$ locally nilpotent derivations. Our approach is based on considering all locally nilpotent derivations commuting with a given derivation. We obtain a characterization of locally nilpotent derivations with a given rank in terms of sets of commuting locally nilpotent derivations. Bibliography: 32 titles.

Авторлар туралы

Nikhilesh Dasgupta

MURTI Research Center, Gandhi Institute of Technology and Management, Bengaluru, Karnataka, India

Хат алмасуға жауапты Автор.
Email: its.nikhilesh@gmail.com

Sergey Gaifullin

Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia; Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia; Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Email: sgayf@yandex.ru
Candidate of physico-mathematical sciences

Әдебиет тізімі

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