A Lie algebra-theoretic approach to characterisation of collision invariants of the Boltzmann equation for general convex particles

<p style='text-indent:20px;'>By studying scattering Lie groups and their associated algebras, we introduce a new method for the characterisation of collision invariants physical families to smooth, convex hard particles in particular case that invariant is class <inline-formula><tex-math id="M1">\begin{document}$ \mathscr{C}^{1} $\end{document}</tex-math></inline-formula>. This work extends Saint-Raymond Wilkinson (<i>Communications on Pure Applied Mathematics</i> (2018), 71(8), pp. 1494–1534), which authors characterise only so-called <i>canonical</i> family. Indeed, our <i>non-canonical</i> scattering, whose existence was reported (<i>Archive Rational Mechanics Analysis</i> (2020), 235(3), 2055–2083). Moreover, improves upon as place no symmetry hypotheses underlying non-spherical make up gas under consideration. The techniques established this paper also yield proof result Boltzmann id="M2">\begin{document}$ $\end{document}</tex-math></inline-formula> classical spheres.</p>