Open Access

# On infinitesimal structure of a hypergroup that originates from a Lie group

### Abstract

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.

### Article Information

 Title On infinitesimal structure of a hypergroup that originates from a Lie group Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 4, 319-329 MathSciNet MR2907360 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

A. A. Kalyuzhnyi
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

G. B. Podkolzin
Ukrainian National Technical University (KPI'), 37, prospect Peremogy, Kyiv, 03056, Ukraine

Yu. A. Chapovsky
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

A. A. Kalyuzhnyi, G. B. Podkolzin, and Yu. A. Chapovsky, On infinitesimal structure of a hypergroup that originates from a Lie group, Methods Funct. Anal. Topology 17 (2011), no. 4, 319-329.

### BibTex

@article {MFAT609,
AUTHOR = {Kalyuzhnyi, A. A. and Podkolzin, G. B. and Chapovsky, Yu. A.},
TITLE = {On infinitesimal structure of   a hypergroup that originates from a Lie group},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {4},
PAGES = {319-329},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=609},
}`