On infinitesimal structure of a hypergroup that originates from a Lie group - Kalyuzhnyi, A. A.; Podkolzin, G. B.; Chapovsky, Yu. A. (Methods of Functional Analysis and Topology, 2011)
We describe an infinitesimal algebra to a hypergroup constructed from a Lie group and a conditional expectation. We also prove a theorem on a decomposition of the conditional expectation into the product of a counital conditional expectation and the one that arises in the double coset construction.