X-Inner Automorphisms of Filtered Algebras. II

1983 ◽  
Vol 87 (4) ◽  
pp. 569
Author(s):  
Susan Montgomery
Keyword(s):  
Filtered Algebras ◽  
Inner Automorphisms

X-Inner Automorphisms of Filtered Algebras

1981 ◽  
Vol 83 (2) ◽  
pp. 263 ◽  
Author(s):  
Susan Montgomery
Keyword(s):  
Filtered Algebras ◽  
Inner Automorphisms

scholarly journals $X$-inner automorphisms of filtered algebras. II

1983 ◽  
Vol 87 (4) ◽  
pp. 569-569
Author(s):  
Susan Montgomery
Keyword(s):  
Filtered Algebras ◽  
Inner Automorphisms

scholarly journals $X$-inner automorphisms of filtered algebras

1981 ◽  
Vol 83 (2) ◽  
pp. 263-263
Author(s):  
Susan Montgomery
Keyword(s):  
Filtered Algebras ◽  
Inner Automorphisms

scholarly journals On Inner Automorphisms Preserving Fixed Subspaces of Clifford Algebras

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Dmitry Shirokov
Keyword(s):  
Clifford Algebras ◽  
Inner Automorphisms

scholarly journals Some properties of the growth and of the algebraic entropy of group endomorphisms

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Anna Giordano Bruno ◽  
Pablo Spiga
Keyword(s):  
Finite Groups ◽  
Addition Theorem ◽  
Finitely Generated ◽  
Growth Type ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Algebraic Entropy ◽  
Finitely Generated Groups ◽  
Identity Automorphism ◽  
Inner Automorphisms

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.

scholarly journals On Continuous Isomorphisms of Topological Groups

1950 ◽  
Vol 1 ◽  
pp. 109-111
Author(s):  
Morikuni Gotô ◽  
Hidehiko Yamabe
Keyword(s):  
Uniform Convergence ◽  
Topological Groups ◽  
Natural Topology ◽  
Locally Compact ◽  
Connected Group ◽  
Inner Automorphisms

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.

scholarly journals Non-inner automorphisms of order p in finite p-groups of coclass 3

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

scholarly journals On inner automorphisms of finite groups

1989 ◽  
Vol 106 (1) ◽  
pp. 87-87 ◽  
Author(s):  
Martin R. Pettet
Keyword(s):  
Finite Groups ◽  
Inner Automorphisms

scholarly journals Powerful p-groups have non-inner automorphisms of order p and some cohomology

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

The structure of norm Clifford algebras

2012 ◽  
Vol 62 (6) ◽  
Author(s):  
Hans Keller ◽  
Herminia Ochsenius
Keyword(s):  
Clifford Algebra ◽  
Classical Case ◽  
Canonical Representation ◽  
Inner Product ◽  
Infinite Products ◽  
Infinite Dimensional ◽  
Significant Step ◽  
Group Of Isometries ◽  
Inner Automorphisms ◽  
Special Case

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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