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On $${\mathbb{F}_q}$$ -Rational Structure of Nilpotent Orbits in the Witt Algebra.

Authors :
Chang, Hao
Yao, Yu-Feng
Source :
Results in Mathematics / Resultate der Mathematik; Feb2014, Vol. 65 Issue 1/2, p181-192, 12p
Publication Year :
2014

Abstract

Let $${\mathfrak{g}=W_1}$$ be the p-dimensional Witt algebra over an algebraically closed field $${k=\overline{\mathbb{F}}_q}$$ , where p > 3 is a prime and q is a power of p. Let G be the automorphism group of $${\mathfrak{g}}$$ . The Frobenius morphism F (resp. $${F_\mathfrak{g}}$$ ) can be defined naturally on G (resp. $${\mathfrak{g}}$$ ). In this paper, we determine the $${F_\mathfrak{g}}$$ -stable G-orbits in $${\mathfrak{g}}$$ . Furthermore, the number of $${\mathbb{F}_q}$$ -rational points in each $${F_\mathfrak{g}}$$ -stable orbit is precisely given. Consequently, we obtain the number of $${\mathbb{F}_q}$$ -rational points in the nilpotent variety. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
14226383
Volume :
65
Issue :
1/2
Database :
Complementary Index
Journal :
Results in Mathematics / Resultate der Mathematik
Publication Type :
Academic Journal
Accession number :
94254913
Full Text :
https://doi.org/10.1007/s00025-013-0339-1