On infinitesimal structure of a hypergroup that originates from a Lie group (Q2896652)

The authors describe an infinitesimal algebra for a hypergroup constructed from a Lie group and a conditional expectation. This hypergroup was introduced by \textit{A. A. Kalyuznyi} [Methods Funct. Anal. Topol. 7, No. 4, 49--68 (2001; Zbl 0992.46059)]; it generalizes the one constructed from an orbital morphism (\textit{R. I. Jewett} [Adv. Math. 18, 1--101 (1975; Zbl 0325.42017)]). The cases of counital conditional expectation and the one arising in the double coset construction are considered. A theorem of decomposition of a conditional expectation into the product of those belonging to the above classes is proved.