Real division algebras with large automorphism group
نویسندگان
چکیده
منابع مشابه
Division Algebras with an Anti-automorphism but with No Involution
In this note we give examples of division rings which posses an anti-automorphism but no involution. The motivation for such examples comes from geometry. If D is a division ring and V a finite-dimensional right D-vector space of dimension ≥ 3, then the projective geometry P(V ) has a duality (resp. polarity) if and only if D has an anti-automorphism (resp. involution) [2, p. 97, p. 111]. Thus,...
متن کاملreal group algebras
in this paper we initiate the study of real group algebras and investigate some of its aspects.let l1 (g) be a group algebra of a locally compact group g,τ :g →g be a group homeomorphismsuch that τ 2 =τοτ = 1, the identity map, and lp (g,τ ) = { f ∈ lp (g) : fοτ = f } ( p ≥ 1) . in thispaper, among other results, we clarify the structure of lp (g,τ ) and characterize amenability ofl1 (g,τ ) and...
متن کاملClassification, Automorphism Groups and Categorical Structure of the Two-Dimensional Real Division Algebras
The category of all 2-dimensional real division algebras is shown to split into four full subcategories each of which is given by the natural action of a Coxeter group of type A1 or A2 on the set of all pairs of ellipses in R which are centred in the origin and have reciprocal axis lengths. Cross-sections for the orbit sets of these group actions are being determined. They yield a classificatio...
متن کامل2 Vertex operator algebras with automorphism group S 3
In this article we study VOAs with two Miyamoto involutions generating S3. In [M3], Miyamoto showed that a VOA generated by two conformal vectors whose Miyamoto involutions generate an automorphism group isomorphic to S3 is isomorphic to one of the four candidates he listed. We construct one of them and prove that our VOA is actually the same as VA(e, f) studied by Miyamoto.
متن کاملFinitely Presented MV-algebras with Finite Automorphism Group
Please see [1] for background on MV-algebras. We address the question, which MV-algebras have finite automorphism group. The automorphism group of the free MV-algebra on 1 generator is just the group of order 2 (folklore). In contrast, it is known that the automorphism group of the free MV-algebra on 2 generators is not even locally finite [4, 2]. Not much else seems to be known. Let us restric...
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: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2004.03.015