X-Inner Automorphisms of Filtered Algebras. II

1983 ◽  
Vol 87 (4) ◽  
pp. 569
Author(s):  
Susan Montgomery

1981 ◽  
Vol 83 (2) ◽  
pp. 263 ◽  
Author(s):  
Susan Montgomery








2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Anna Giordano Bruno ◽  
Pablo Spiga

AbstractWe study the growth of group endomorphisms, a generalization of the classical notion of growth of finitely generated groups, which is strictly related to algebraic entropy. We prove that the inner automorphisms of a group have the same growth type and the same algebraic entropy as the identity automorphism. Moreover, we show that endomorphisms of locally finite groups cannot have intermediate growth. We also find an example showing that the Addition Theorem for algebraic entropy does not hold for endomorphisms of arbitrary groups.



1950 ◽  
Vol 1 ◽  
pp. 109-111
Author(s):  
Morikuni Gotô ◽  
Hidehiko Yamabe

Let G be a locally compact connected group, and let A (G) be the group of all continuous automorphisms of G. We shall introduce a natural topology into A(G) as previously (i.e. the topology of uniform convergence in the wider sense.) When the component of the identity of A(G) coincides with the group of inner automorphisms, we shall call G complete. The purpose of this note is to prove the following theorem and give some applications of it.



2016 ◽  
Vol 183 (4) ◽  
pp. 679-697 ◽  
Author(s):  
Marco Ruscitti ◽  
Leire Legarreta ◽  
Manoj K. Yadav
Keyword(s):  


1989 ◽  
Vol 106 (1) ◽  
pp. 87-87 ◽  
Author(s):  
Martin R. Pettet


2010 ◽  
Vol 323 (3) ◽  
pp. 779-789 ◽  
Author(s):  
Alireza Abdollahi
Keyword(s):  


2012 ◽  
Vol 62 (6) ◽  
Author(s):  
Hans Keller ◽  
Herminia Ochsenius

AbstractOrthomodular Hilbertian spaces are infinite-dimensional inner product spaces (E, 〈·, ·〉) with the rare property that to every orthogonally closed subspace U ⊆ E there is an orthogonal projection from E onto U. These spaces, discovered about 30 years ago, are constructed over certain non-Archimedeanly valued, complete fields and are endowed with a non-Archimedean norm derived from the inner product. In a previous work [KELLER, H. A.—OCHSENIUS, H.: On the Clifford algebra of orthomodular spaces over Krull valued fields. In: Contemp. Math. 508, Amer. Math. Soc., Providence, RI, 2010, pp. 73–87] we described the construction of a new object, called the norm Clifford algebra C̃(E) associated to E. It can be considered a counterpart of the well-established Clifford algebra of a finite dimensional quadratic space. In contrast to the classical case, C̃(E) allows to represent infinite products of reflections by inner automorphisms. It is a significant step towards a better understanding of the group of isometries, which in infinite dimension is complex and hard to grasp.In the present paper we are concerned with the inner structure of these new algebras. We first give a canonical representation of the elements, and we prove that C̃ is always central. Then we focus on an outstanding special case in which C̃ is shown to be a division ring. Moreover, in that special case we completely describe the ideals of the corresponding valuation ring $$\mathcal{A}$$. It turns out, rather unexpectedly, that every left-ideal and every right-ideal of $$\mathcal{A}$$ is in fact bilateral.



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