Let $M$ be a Riemannian manifold. We denote by $\mathfrak{g}$ the space of all smooth function $f:TM\to \mathbb{R}$ with fibre wise polynomial growth. Is it a Lie algebra? What is a precise infinite dimensional Lie group bwhose Lie algebra is the above $\mathfrak{g}$? Is the Lie algebra structure mentioned above independent of choosing Riemanian metric?
A Lie group whose Lie algebra is the (Lie algebra?) of all functions with fibrewise polynomial growth
Ali Taghavi
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