Composition series in Chevalley algebras
نویسندگان
چکیده
منابع مشابه
Jordan-chevalley Decomposition in Finite Dimesional Lie Algebras
Let g be a finite dimensional Lie algebra over a field k of characteristic zero. An element x of g is said to have an abstract Jordan-Chevalley decomposition if there exist unique s, n ∈ g such that x = s + n, [s, n] = 0 and given any finite dimensional representation π : g → gl(V ) the Jordan-Chevalley decomposition of π(x) in gl(V ) is π(x) = π(s) + π(n). In this paper we prove that x ∈ g has...
متن کاملNonexistence of Reflexive Ideals in Iwasawa Algebras of Chevalley Type
Let Φ be a root system and let Φ(Zp) be the standard Chevalley Zp-Lie algebra associated to Φ. For any integer t > 1, let G be the uniform pro-p group corresponding to the powerful Lie algebra pΦ(Zp) and suppose that p > 5. Then the Iwasawa algebra ΩG has no nontrivial reflexive ideals. This was previously proved by authors for the root system A1.
متن کاملAutomorphisms and Isomorphisms of Chevalley Groups and Algebras
Suppose that Φ is a reduced irreducible root system, R is an associative commutative ring with unity, G(Φ, R) is the corresponding adjoint Chevalley group, and E(Φ, R) is its elementary subgroup (see Section 5). There are a lot of results (see, e.g., [Wat80], [Pet82], [GMi83], [HO’M89], [Abe93], [Che00], [Bun07], and references therein*) asserting that, under some conditions, all automorphisms ...
متن کاملFactorization in the Composition Algebras
Let O be a maximal arithmetic in one of the four (non-split) composition algebras over R, and let ] = mn be the norm of an element in O. Rehm 15] describes an algorithm for nding all factorizations of as = , where ] = m, ] = n and (m; n) = 1. Here, we extend the algorithm to general , m, and n, providing precise geometrical conngurations for the sets of left-and right-hand divisors.
متن کاملNotes on composition algebras
In each of these dimensions examples always exist, and we find out a great deal about the examples as well. Indeed, if we were only interested in a proof of the theorem, then the usual doubling methods (see [6] or Section 6.4 below) are quicker. We also wish to study carefully the related geometries (and groups, although we do not really get to them much). Hurwitz’ theorem does not require the ...
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: Pacific Journal of Mathematics
سال: 1970
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1970.32.429