Automorphism group
View article: The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry codes
The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry codes Open
In this manuscript, we investigate the automorphism group of a maximal function field with the second largest possible genus over finite field of even characteristic, which is called the Abdón--Torres function field. As an application, we …
View article: The Enriques surface of minimal entropy
The Enriques surface of minimal entropy Open
Lehmer's number $λ_{10}$ is the smallest dynamical degree greater than $1$ that can occur for an automorphism of an algebraic surface. We show that $λ_{10}$ cannot be realized by automorphisms of Enriques surfaces in odd characteristic, ex…
View article: Complete toric varieties with semisimple automorphism group
Complete toric varieties with semisimple automorphism group Open
Let $X$ be a complete toric variety. We give a criterion to decide whether $X$ decomposes as a product of complete toric varieties by analyzing the $1$-skeleton of its fan. More precisely, we prove that any direct-sum decomposition of the …
View article: Construction of directed strongly regular graphs with nontrivial automorphisms
Construction of directed strongly regular graphs with nontrivial automorphisms Open
View article: Moduli Spaces of Non-commutative Rings and Their Automorphism Groups
Moduli Spaces of Non-commutative Rings and Their Automorphism Groups Open
This paper explores the intricate landscape of moduli spaces associated with non-commutative rings and the inherent structures of their automorphism groups. Constructing and analyzing such moduli spaces presents significant challenges. The…
View article: Moduli Spaces of Non-commutative Rings and Their Automorphism Groups
Moduli Spaces of Non-commutative Rings and Their Automorphism Groups Open
This paper explores the intricate landscape of moduli spaces associated with non-commutative rings and the inherent structures of their automorphism groups. Constructing and analyzing such moduli spaces presents significant challenges. The…
View article: Symbolic computation of optimal systems of subalgebras of three- and four-dimensional real Lie algebras
Symbolic computation of optimal systems of subalgebras of three- and four-dimensional real Lie algebras Open
The complete optimal systems of subalgebras of all nonisomorphic three- and four-dimensional real Lie algebras are analyzed by the program SymboLie running in the computer algebra system Wolfram Mathematica\texttrademark. The approach uses…
View article: Symbolic computation of optimal systems of subalgebras of three- and four-dimensional real Lie algebras
Symbolic computation of optimal systems of subalgebras of three- and four-dimensional real Lie algebras Open
The complete optimal systems of subalgebras of all nonisomorphic three- and four-dimensional real Lie algebras are analyzed by the program SymboLie running in the computer algebra system Wolfram Mathematica\texttrademark. The approach uses…
View article: Peano's Infinite Mirrors: Automorphism Groups of Non-Standard Models
Peano's Infinite Mirrors: Automorphism Groups of Non-Standard Models Open
This paper explores the intricate structure of automorphism groups of non-standard models of Peano Arithmetic (PA), conceptualizing them as "Peano's Infinite Mirrors". Non-standard models, rich and complex structures extending the natural …
View article: Height zero characters and Galois automorphisms
Height zero characters and Galois automorphisms Open
Let $G$ be a finite group and let $p$ be a prime. In this paper, we prove a strengthened version of Brauer's height zero conjecture for the principal $p$-block of $G$ that takes the action of a certain group of Galois automorphisms into ac…
View article: Peano's Infinite Mirrors: Automorphism Groups of Non-Standard Models
Peano's Infinite Mirrors: Automorphism Groups of Non-Standard Models Open
This paper explores the intricate structure of automorphism groups of non-standard models of Peano Arithmetic (PA), conceptualizing them as "Peano's Infinite Mirrors". Non-standard models, rich and complex structures extending the natural …
View article: Moduli Spaces of Non-commutative Rings and Their Automorphism Groups
Moduli Spaces of Non-commutative Rings and Their Automorphism Groups Open
This paper explores the intricate landscape of moduli spaces associated with non-commutative rings and the inherent structures of their automorphism groups. Constructing and analyzing such moduli spaces presents significant challenges. The…
View article: Height zero characters and Galois automorphisms
Height zero characters and Galois automorphisms Open
Let $G$ be a finite group and let $p$ be a prime. In this paper, we prove a strengthened version of Brauer's height zero conjecture for the principal $p$-block of $G$ that takes the action of a certain group of Galois automorphisms into ac…
View article: The automorphism groups and identification of some Generalized Paley Graphs
The automorphism groups and identification of some Generalized Paley Graphs Open
The family of generalized Paley graphs of prime power order $q$ and degree $(q-1)/k$ is studied. It is shown that the automorphism group of a graph in this family is a subgroup of ${\mathrm{AΓL}}(1,q)$ whenever $q$ is sufficiently large re…
View article: The automorphism groups and identification of some Generalized Paley Graphs
The automorphism groups and identification of some Generalized Paley Graphs Open
The family of generalized Paley graphs of prime power order $q$ and degree $(q-1)/k$ is studied. It is shown that the automorphism group of a graph in this family is a subgroup of ${\mathrm{AΓL}}(1,q)$ whenever $q$ is sufficiently large re…
View article: Peano's Infinite Mirrors: Automorphism Groups of Non-Standard Models
Peano's Infinite Mirrors: Automorphism Groups of Non-Standard Models Open
This paper explores the intricate structure of automorphism groups of non-standard models of Peano Arithmetic (PA), conceptualizing them as "Peano's Infinite Mirrors". Non-standard models, rich and complex structures extending the natural …
View article: Stabilizing Automorphisms of Quantum Affine Space
Stabilizing Automorphisms of Quantum Affine Space Open
We examine the graded automorphism groups of quantum affine spaces and classify these groups for spaces of dimension 7 or less. Using permutation actions on partitions, we investigate cases when the group decomposes as a product of graded …
View article: Algebraic curves with a large cyclic automorphism group
Algebraic curves with a large cyclic automorphism group Open
View article: Stabilizing Automorphisms of Quantum Affine Space
Stabilizing Automorphisms of Quantum Affine Space Open
We examine the graded automorphism groups of quantum affine spaces and classify these groups for spaces of dimension 7 or less. Using permutation actions on partitions, we investigate cases when the group decomposes as a product of graded …
View article: Equilibrium stresses in frameworks via symmetric averaging
Equilibrium stresses in frameworks via symmetric averaging Open
For a bar-joint framework $$(G,\textbf{p})$$ , a subgroup $$\Gamma $$ of the automorphism group of G , and a subgroup of the orthogonal group isomorphic to $$\Gamma $$ , we introduce a symmetric averaging map which produces a ba…
View article: A note on zero-cycles on bielliptic surfaces
A note on zero-cycles on bielliptic surfaces Open
We study the Chow group of zero-cycles $\text{CH}_0(S)$ of a bielliptic surface $S=(E_1\times E_2)/G$, where $E_1, E_2$ are elliptic curves and $G$ is a finite group acting on $E_1$ by translations and on $E_2$ by automorphisms such that $…
View article: A note on zero-cycles on bielliptic surfaces
A note on zero-cycles on bielliptic surfaces Open
We study the Chow group of zero-cycles $\text{CH}_0(S)$ of a bielliptic surface $S=(E_1\times E_2)/G$, where $E_1, E_2$ are elliptic curves and $G$ is a finite group acting on $E_1$ by translations and on $E_2$ by automorphisms such that $…
View article: Equivariant embeddings of Riemann surfaces in Euclidean spaces with minimal dimensions
Equivariant embeddings of Riemann surfaces in Euclidean spaces with minimal dimensions Open
Let $Σ_g$ be a closed Riemann surface of genus $g$. Let $G$ be a finite subgroup of the automorphism group of $Σ_g$. It is well known that there exists a smooth $G$-equivariant embedding from $Σ_g$ to some Euclidean space $\mathbb{R}^n$. L…
View article: Equivariant embeddings of Riemann surfaces in Euclidean spaces with minimal dimensions
Equivariant embeddings of Riemann surfaces in Euclidean spaces with minimal dimensions Open
Let $Σ_g$ be a closed Riemann surface of genus $g$. Let $G$ be a finite subgroup of the automorphism group of $Σ_g$. It is well known that there exists a smooth $G$-equivariant embedding from $Σ_g$ to some Euclidean space $\mathbb{R}^n$. L…
View article: Endomorphism and automorphism graphs of finite groups
Endomorphism and automorphism graphs of finite groups Open
Let $G$ be a group. The directed endomorphism graph, $\dend(G)$ of $G$ is a directed graph with vertex set $G$ and there is a directed edge from the vertex $a$ to the vertex $b$ if $a \neq b$ and there exists an endomorphism on $G$ mapping…
View article: Some Results on Bichon's Quantum Automorphism Group of Graphs
Some Results on Bichon's Quantum Automorphism Group of Graphs Open
The notion of the quantum automorphism group of a graph was introduced by J. Bichon in 2003 and T. Banica in 2005 respectively. This article explores primarily the quantum automorphism group of a graph $Γ$, denoted by $QAut_{Bic}(Γ)$, in B…
View article: Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates
Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates Open
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge theor…
View article: Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates
Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates Open
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge theor…
View article: Some Results on Bichon's Quantum Automorphism Group of Graphs
Some Results on Bichon's Quantum Automorphism Group of Graphs Open
The notion of the quantum automorphism group of a graph was introduced by J. Bichon in 2003 and T. Banica in 2005 respectively. This article explores primarily the quantum automorphism group of a graph $Γ$, denoted by $QAut_{Bic}(Γ)$, in B…
View article: Dynamics of Dehn Twists in the Outer Automorphism Group of a Free Group
Dynamics of Dehn Twists in the Outer Automorphism Group of a Free Group Open
We study Dehn twists in the outer automorphism group of a finitely generated non-abelian free group. Our main result states that, under certain compatibility conditions, sufficiently large powers of finitely many Dehn twists generate a rig…