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\fancyhead[HCO]{9th Int. Conf. on Mathematics and Informatics,
	September 7-8, 2023, T\^argu Mure\c s, Romania}
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\begin{document}

\begin{center}{\Large\bf
Tangent algebra of a diffeomorphism group and its application
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\begin{center}{\large\bf\noindent
Z. Muzsnay
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Department of Geometry, University of Debrecen
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muzsnay@science.unideb.hu
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\vspace*{7mm}
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In this talk the notion of the tangent algebra of a (not necessarily
smooth) subgroup of the diffeomorphism group $Diff (M)$ of a compact
manifold $M$ is introduced.  We prove that this tangent algebra is a Lie
subalgebra of the Lie algebra of smooth vector fields on $M$. The
construction can be generalized to subgroups of any (finite or infinite
dimensional) Lie groups.  The tangent Lie algebra introduced this way is a
generalization of the classical Lie algebra in the smooth case.  As a
working example, we discuss in detail the tangent structure of the holonomy
group and the fibered holonomy group of Finsler manifolds.

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