Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Classification of generalized Witt algebras over algebraically closed fields


Author: Robert Lee Wilson
Journal: Trans. Amer. Math. Soc. 153 (1971), 191-210
MSC: Primary 17B20; Secondary 16A72
MathSciNet review: 0316523
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \Phi $ be a field of characteristic $ p > 0$ and $ m,{n_1}, \ldots ,{n_m}$ be integers $ \geqq 1$. A Lie algebra $ W(m:{n_1}, \ldots ,{n_m})$ over $ \Phi $ is defined. It is shown that if $ \Phi $ is algebraically closed then $ W(m:{n_1}, \ldots ,{n_m})$ is isomorphic to a generalized Witt algebra, that every finite-dimensional generalized Witt algebra over $ \Phi $ is isomorphic to some $ W(m:{n_1}, \ldots ,{n_m})$, and that $ W(m:{n_1}, \ldots ,{n_m})$ is isomorphic to $ W(s:{r_1}, \ldots ,{r_s})$ if and only if $ m = s$ and $ {r_i} = {n_{\sigma (i)}}$ for $ 1 \leqq i \leqq m$ where $ \sigma $ is a permutation of $ \{ 1, \ldots ,m\} $. This gives a complete classification of the finite-dimensional generalized Witt algebras over algebraically closed fields. The automorphism group of $ W(m:{n_1}, \ldots ,{n_m})$ is determined for $ p > 3$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 17B20, 16A72

Retrieve articles in all journals with MSC: 17B20, 16A72


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0316523-6
PII: S 0002-9947(1971)0316523-6
Keywords: Generalized Witt algebras
Article copyright: © Copyright 1971 American Mathematical Society