1. Spectral synthesis for coadjoint orbits of nilpotent Lie groups
- Author
-
Jean Ludwig, Ingrid Beltiţă, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and The first author has been partially supported by the Grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0131.
- Subjects
Spectral synthesis ,General Mathematics ,Minimal ideal ,01 natural sciences ,Combinatorics ,Coadjoint orbit ,Mathematics Subject Classification Primary 43A45 Secondary 43A20 22E25 22E27 ,Primary ideal ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,[MATH]Mathematics [math] ,0101 mathematics ,Invariant (mathematics) ,Representation Theory (math.RT) ,Primary 43A45, Secondary 43A20, 22E25, 22E27 ,ComputingMilieux_MISCELLANEOUS ,0105 earth and related environmental sciences ,Mathematics ,Discrete mathematics ,010505 oceanography ,010102 general mathematics ,Lie group ,Group algebra ,16. Peace & justice ,Linear subspace ,Nilpotent ,Mathematics - Classical Analysis and ODEs ,Nilpotent Lie group ,Mathematics - Representation Theory - Abstract
We determine the space of primary ideals in the group algebra $L^1(G)$ of a connected nilpotent Lie group by identifying for every $\pi\in\hat G $ the family ${\mathcal I}^\pi $ of primary ideals with hull $\{\pi\}$ with the family of invariant polynomials of a certain finite dimensional subspace ${\mathcal P}_Q^\pi $ of the space of polynomials ${\mathcal P}(G) $ on $G $., Comment: 25 pages
- Published
- 2014
- Full Text
- View/download PDF