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Supports of weight modules over Witt algebras
- Source :
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 141:155-170
- Publication Year :
- 2011
- Publisher :
- Cambridge University Press (CUP), 2011.
-
Abstract
- In this paper, as the first step towards classification of simple weight modules with finite dimensional weight spaces over Witt algebras $W_n$, we explicitly describe supports of such modules. We also obtain some descriptions on the support of an arbitrary simple weight module over a $\Z^n$-graded Lie algebra $\mathfrak{g}$ having a root space decomposition $\oplus_{\alpha\in\Z^n}\mathfrak {g}_\alpha$ with respect to the abelian subalgebra $\mathfrak {g}_0$, with the property $[\mathfrak{g}_\alpha,\mathfrak {g}_\beta]= \mathfrak {g}_{\alpha+\beta}$ for all $\alpha,\beta\in\Z^n$, $\alpha\neq \beta$ (this class contains the algebra $W_n$).<br />Comment: 17 pages
- Subjects :
- General Mathematics
Mathematics::Rings and Algebras
010102 general mathematics
01 natural sciences
Algebra
Simple (abstract algebra)
17B10, 17B20, 17B65, 17B66, 17B68
0103 physical sciences
FOS: Mathematics
010307 mathematical physics
Representation Theory (math.RT)
0101 mathematics
Mathematics::Representation Theory
Mathematics - Representation Theory
Mathematics
Subjects
Details
- ISSN :
- 14737124 and 03082105
- Volume :
- 141
- Database :
- OpenAIRE
- Journal :
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Accession number :
- edsair.doi.dedup.....e3494344139ca80b8e2cc17387a3e358