A solution that uses all the tools of titlesec:
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[textwidth=140mm, textheight=213mm, marginratio={4:6,5:7}]{geometry}
\usepackage{amsmath, amsfonts, amssymb}
\DeclareMathOperator\GL{\mathfrak{gl}}
\DeclareMathOperator\chr{char}
\usepackage[noindentafter]{titlesec}
\titleformat{\section}[block]{\filcenter\scshape}{\thesection.}{0.5em}{}
\titlespacing*{\section}{0pt}{2\baselineskip}{1\baselineskip}
\begin{document}
\section{Introduction}
Let $ L $ be a finite dimensional Lie algebra over the field $ F $. By a finite-dimensional representation, we mean a Lie algebra homomorphism $ φ \colon L → \GL(V)$ for some vector space $ V $ with $ \dim V < ∞ $. When $ φ $ is injective, $ φ $ is said to be a \emph{faithful} representation. If $ L $ has a faithful representation, then we can view elements of $ L$ as matrices with entries in $ F $. It is natural to ask whether every finite dimensional Lie algebra can be concretely realized in this way. Ado [1] gave an affirmative answer when $ \chr(F) = 0$. The result was extended by Iwasawa [2] to cover the case $ \chr(F) = p $ for prime $ p $. We follow Fulton and Harris [3] to give the proof for the case $ \chr(F) = 0 $.
\section{Universal Enveloping Algebras}
\end{document}

titlessecand theblockstyle for sections. Details in the documentation. – Bernard Dec 07 '14 at 23:29