The purpose of this article is twofold. The first aim is to characterize h-extendibility of smoothly bounded pseudoconvex domains in Cn+1 by their noncompact automorphism groups. Our second goal is ...to show that if the squeezing function tends to 1 at an h-extendible boundary point of a smooth pseudoconvex domain in Cn+1, then this point must be strongly pseudoconvex.
We show that there is a distortion element in a finitely generated subgroup G of the automorphism group of the full shift, namely an element of infinite order whose word norm grows ...polylogarithmically. As a corollary, we obtain a lower bound on the entropy dimension of any subshift containing a copy of G, and that a sofic shift’s automorphism group contains a distortion element if and only if the sofic shift is uncountable. We obtain also that groups of Turing machines and the higher-dimensional Brin–Thompson groups
$mV$
admit distortion elements; in particular,
$2V$
(unlike V) does not admit a proper action on a CAT
$(0)$
cube complex. In each case, the distortion element roughly corresponds to the SMART machine of Cassaigne, Ollinger, and Torres-Avilés A small minimal aperiodic reversible Turing machine. J. Comput. System Sci. 84 (2017), 288–301.
Coble surfaces in characteristic two KATSURA, Toshiyuki; KONDŌ, Shigeyuki
Journal of the Mathematical Society of Japan,
2023, Letnik:
75, Številka:
4
Journal Article
Let C be an irreducible plane curve of PG(2,K) where K is an algebraically closed field of characteristic p≥0. A point Q∈C is an inner Galois point for C if the projection πQ from Q is Galois. Assume ...that C has two different inner Galois points Q1 and Q2, both simple. Let G1 and G2 be the respective Galois groups. Under the assumption that Gi fixes Qi, for i=1,2, we provide a complete classification of G=〈G1,G2〉 and we exhibit a curve for each such G. Our proof relies on deeper results from group theory.
We study and classify the 3-dimensional Hom-Lie algebras over C. We provide first a complete set of representatives for the isomorphism classes of skew-symmetric bilinear products defined on a ...3-dimensional complex vector space g. The well known Lie brackets for the 3-dimensional Lie algebras are included into appropriate isomorphism classes of such products representatives. For each product representative, we provide a complete set of canonical forms for the linear maps g→g that turn g into a Hom-Lie algebra, thus characterizing the corresponding isomorphism classes. As by-products, Hom-Lie algebras for which the linear maps g→g are not homomorphisms for their products are exhibited. Examples also arise of non-isomorphic families of Hom-Lie algebras which share, however, a fixed Lie-algebra product on g. In particular, this is the case for the complex simple Lie algebra sl2(C). Similarly, there are isomorphism classes for which their skew-symmetric bilinear products can never be Lie algebra brackets on g.
Let
denote the number of orbits on the elements of a group G under the action of its automorphism group. We determine all finite simple groups G such that
On twists of smooth plane curves Badr, Eslam; Bars Cortina, Francesc; Lorenzo García, Elisa
Mathematics of computation,
01/2019, Letnik:
88, Številka:
315
Journal Article
Recenzirano
Odprti dostop
Given a smooth curve defined over a field k that admits a non-singular plane model over \overline {k}, a fixed separable closure of k, it does not necessarily have a non-singular plane model defined ...over the field k. We determine under which conditions this happens and we show an example of such phenomenon: a curve defined over k admitting plane models but none defined over k. Now, even assuming that such a smooth plane model exists, we wonder about the existence of non-singular plane models over k for its twists. We characterize twists possessing such models and we also show an example of a twist not admitting any non-singular plane model over k. As a consequence, we get explicit equations for a non-trivial Brauer-Severi surface. Finally, we obtain a theoretical result to describe all the twists of smooth plane curves with cyclic automorphism group having a model defined over k whose automorphism group is generated by a diagonal matrix.
We prove that for any transitive subshift X with word complexity function
$c_n(X)$
, if
$\liminf ({\log (c_n(X)/n)}/({\log \log \log n})) = 0$
, then the quotient group
${{\mathrm {Aut}(X,\sigma ...)}/{\langle \sigma \rangle }}$
of the automorphism group of X by the subgroup generated by the shift
$\sigma $
is locally finite. We prove that significantly weaker upper bounds on
$c_n(X)$
imply the same conclusion if the gap conjecture from geometric group theory is true. Our proofs rely on a general upper bound for the number of automorphisms of X of range n in terms of word complexity, which may be of independent interest. As an application, we are also able to prove that for any subshift X, if
${c_n(X)}/{n^2 (\log n)^{-1}} \rightarrow 0$
, then
$\mathrm {Aut}(X,\sigma )$
is amenable, improving a result of Cyr and Kra. In the opposite direction, we show that for any countable infinite locally finite group G and any unbounded increasing
$f: \mathbb {N} \rightarrow \mathbb {N}$
, there exists a minimal subshift X with
${{\mathrm {Aut}(X,\sigma )}/{\langle \sigma \rangle }}$
isomorphic to G and
${c_n(X)}/{nf(n)} \rightarrow 0$
.
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