Classification of generalized Witt algebras over algebraically closed fields
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- by Robert Lee Wilson PDF
- Trans. Amer. Math. Soc. 153 (1971), 191-210 Request permission
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
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 153 (1971), 191-210
- MSC: Primary 17B20; Secondary 16A72
- DOI: https://doi.org/10.1090/S0002-9947-1971-0316523-6
- MathSciNet review: 0316523