Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1128.17007
Aslaksen, Helmer; Lang, Mong Lung
Extending $\pi$-systems to bases of root systems. (English)
[J] J. Algebra 287, No. 2, 496-500 (2005). ISSN 0021-8693

Summary: Let $R$ be an indecomposable root system. It is well known that any root is part of a basis $B$ of $R$. But when can you extend a set, $C$, of two or more roots to a basis $B$ of $R$? A $\pi$-system is a linearly independent set of roots such that if $\alpha$ and $\beta$ are in $C$, then $\alpha-\beta$ is not a root. We will use results of Dynkin and Bourbaki to show that with two exceptions, $A_3\subset B_n$ and $A_7\subset E_8$, an indecomposable $\pi$-system whose Dynkin diagram is a subdiagram of the Dynkin diagrams of $R$ can always be extended to a basis of $R$.

MSC 2000:: *17B20 Simple and semisimple Lie algebras

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.
	Elementary number theory. Primes, congruences, and secrets.

Simple Search

Zentralblatt MATH Berlin [Germany]