منابع مشابه
Completely reducible sets
We study the family of rational sets of words, called completely reducible and which are such that the syntactic representation of their characteristic series is completely reducible. This family contains, by a result of Reutenauer, the submonoids generated by bifix codes and, by a result of Berstel and Reutenauer, the cyclic sets. We study the closure properties of this family. We prove a resu...
متن کاملCompletely Reducible Lie Subalgebras
Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H ≤ G. In this note, we give a notion of G-complete reducibility – G-cr for short – for Lie subalgebras of Lie(G), and we show that if the smooth subgroup H < G is G-cr, then Lie(H) is G-cr as well.
متن کاملCompletely Reducible p-compact Groups
Rational automorphisms of products of simple p-compact groups are shown to be composites of products of rational automorphisms of the individual factors and permutation maps.
متن کاملGenerating Finite Completely Reducible Linear Groups
It is proved here that each finite completely reducible linear group of dimension d (over an arbitrary field) can be generated by L 3 d] elements. If a finite linear group G of dimension d is not completely reducible, then its characteristic is a prime, p say, and the factor group of G modulo the largest normal p-subgroup O.p(G) may be viewed as a completely reducible linear group acting on the...
متن کاملInvariant Algebras and Completely Reducible Representations
We give a general construction of affine noetherian algebras with the property that every finite dimensional representation is completely reducible. Starting from enveloping algebras of semi simple Lie algebras in characteristic zero we obtain explicit examples and describe some of their properties. In the following an algebra A will always mean an associative algebra over a field k with a unit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1968
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1968-0231234-9