Search results for "Automorphism"
showing 8 items of 88 documents
A Series of Hadamard Designs with Large Automorphism Groups
2000
Abstract Whilst studying a certain symmetric (99, 49, 24)-design acted upon by a Frobenius group of order 21, it became clear that the design would be a member of an infinite series of symmetric (2q2 + 1, q2, (q2 − 1)/2)-designs for odd prime powers q. In this note, we present the definition of the series and give some information about the automorphism groups of its members.
Characterization of strong chain geometries by their automorphism group
1992
A wide class of chain geometries is characterized by their automorphism group using properties of a distinguished involution.
Algebraic singularities have maximal reductive automorphism groups
1989
LetX = On/ibe an analytic singularity where ṫ is an ideal of theC-algebraOnof germs of analytic functions on (Cn, 0). Letdenote the maximal ideal ofXandA= AutXits group of automorphisms. An abstract subgroupequipped with the structure of an algebraic group is calledalgebraic subgroupofAif the natural representations ofGon all “higher cotangent spaces”are rational. Letπbe the representation ofAon the first cotangent spaceandA1=π(A).
The action of a compact Lie group on nilpotent Lie algebras of type {{n,2}}
2015
Abstract We classify finite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO 2 ( ℝ ) ${{\mathrm{SO}}_{2}(\mathbb{R})}$ . This is the first step to extend the class of nilpotent Lie algebras 𝔥 ${{\mathfrak{h}}}$ of type { n , 2 } ${\{n,2\}}$ to solvable Lie algebras in which 𝔥 ${{\mathfrak{h}}}$ has codimension one.
Embeddings of Danielewski hypersurfaces
2008
In this thesis, we study a class of hypersurfaces in $\mathbb{C}^3$, called \emph{Danielewski hypersurfaces}. This means hypersurfaces $X_{Q,n}$ defined by an equation of the form $x^ny=Q(x,z)$ with $n\in\mathbb{N}_{\geq1}$ and $\deg_z(Q(x,z))\geq2$. We give their complete classification, up to isomorphism, and up to equivalence via an automorphism of $\mathbb{C}^3$. In order to do that, we introduce the notion of standard form and show that every Danielewski hypersurface is isomorphic (by an algorithmic procedure) to a Danielewski hypersurface in standard form. This terminology is relevant since every isomorphism between two standard forms can be extended to an automorphism of the ambiant …
The Abelian Kernel of an Inverse Semigroup
2020
The problem of computing the abelian kernel of a finite semigroup was first solved by Delgado describing an algorithm that decides whether a given element of a finite semigroup S belongs to the abelian kernel. Steinberg extended the result for any variety of abelian groups with decidable membership. In this paper, we used a completely different approach to complete these results by giving an exact description of the abelian kernel of an inverse semigroup. An abelian group that gives this abelian kernel was also constructed.
Automorphisms of right-angled Artin groups
2012
The purpose of this thesis is to study the automorphisms of right-angled Artin groups. Given a finite simplicial graph $\Gamma$, the right-angled Artin group $G_\Gamma$ associated to $\Gamma$ is the group defined by the presentation whose generators are the vertices of $\Gamma$, and whose relators are commutators of pairs of adjacent vertices. The first chapter is intended as a general introduction to the theory of right-angled Artin groups and their automorphisms. In a second chapter, we prove that every subnormal subgroup of $p$-power index in a right-angled Artin group is conjugacy $p$-separable. As an application, we prove that every right-angled Artin group is conjugacy separable in th…
Counting Berg partitions via Sturmian words and substitution tilings
2013
We develop the connection of Berg partitions with special substitution tilings of two tiles. We obtain a new proof that the number of Berg partitions with a fixed connectivity matrix is equal to half of the sum of its entries, [12]. This approach together with the formula of Seebold [10], for the number of substitutions preserving a given Sturmian sequence, shows that all of the combinatorial substitutions can be realized geometrically as Berg partitions. We treat Sturmian tilings as intersection tilings of bi-partitions. Using the symmetries of bi-partitions we obtain geometrically the palindromic properties of Sturmian sequences (Theorem 3) established combinatorially by de Luca and Migno…