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# An Explicit Cell Decomposition of the Wonderful Compactification of a Semisimple Algebraic Group

Published:2003-03-01
Printed: Mar 2003
• Lex E. Renner
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## Abstract

We determine an explicit cell decomposition of the wonderful compactification of a semi\-simple algebraic group. To do this we first identify the $B\times B$-orbits using the generalized Bruhat decomposition of a reductive monoid. From there we show how each cell is made up from $B\times B$-orbits.
 MSC Classifications: 14L30 - Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 14M17 - Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15] 20M17 - Regular semigroups