Narrow Results

Let $G$ be a graph with vertex set $V(G)$, $f$ a permutation of $V(G)$. Define ${\delta }_f(x,y)=|d(x,y)-d(f(x),f(y))|$ and ${\delta }_f(G)=\sum {\delta }_f(x,y)$, where the sum is taken over all unordered pairs $x$, $y$ of distinct vertices of $G$. Let $\pi (G)$ denote the smallest positive value of ${\delta }_f(G)$ among all permutations $f$ of $V(G)$. A permutation $f$ with ${\delta }_f(G)=\pi (G)$ is called a near automorphism of $G$. In this paper, the near automorphisms of the complement or the square of a cycle are characterized. Moreover, $\pi (\overline{C_n})$ and $\pi \left(C_n^2\right)$ are determined.

In this paper, we study automorphisms of finitely generated free metabelian Novikov algebras and show that every tame automorphism of a two-generated free right nilpotent Novikov algebra of index 3 is simple reducible. We offer a method on recognizing automorphisms of finitely generated free metabelian Novikov algebras by using the theory of Gröbner–Shirshov basis.

In this paper, we introduce the notions of crossed modules of associative conformal algebras, two-term strongly homotopy associative conformal algebras, and discuss the relationship between them and the third Hochschild cohomology of associative conformal algebras. We classify the non-abelian extensions by introducing the non-abelian cohomology. We show that non-abelian extensions of an associative conformal algebra can be viewed as Maurer–Cartan elements of a suitable differential graded Lie algebra, and prove that there is a one-one correspondence between the Deligne groupoid of this differential graded Lie algebra and the non-abelian cohomology. For any two associative conformal algebras $A$ and $B$, we provide the condition that a pair of automorphisms in Aut(A) × Aut(B) can be extended to an automorphisms of the non-abelian extension algebra of $B$ by $A$, and give the fundamental sequence of Wells in the context of associative conformal algebras.

This paper investigates the algebraic properties of the Bondi–Metzner–Sachs (BMS) superalgebra, as initially introduced by G. Barnich, L. Donnay, J. Matulich and R. Troncoso, Asymptotic symmetries and dynamics of 3D flat supergravity, J. High Energy Phys.2014 (2014) 071. We introduce a new realization of the BMS superalgebra using the Balinsky–Novikov construction. Utilizing this approach, we prove that the BMS superalgebra constitutes the unique minimal supersymmetric extension of the BMS algebra in three dimensions. Additionally, we compute the low-order cohomology groups of the BMS superalgebra and classify its derivations, central extensions, and automorphisms.

We show that for any finite group $G$, there exist infinitely many simple anticommutative algebras with multiplicative bases $(𝔄,\mathcal{ℬ})$ such that the group $\mathrm{\text{Aut}}((𝔄,\mathcal{ℬ}))$ is isomorphic to $G$.

For a flow α on a C*-algebra one defines a symmetry as the group of automorphisms γ such that γαγ^-1 is a cocycle perturbation of α. We propose to define a core of this symmetry, which acts trivially on the set of equivalence classes of KMS state representations, but may act non-trivially on the set of equivalence classes of covariant irreducible representations. In particular this core acts transitively on the set of those which induce faithful representations of the crossed product by α.

Let G be an inductive limit of finite cyclic groups, and A be a unital simple projectionless C*-algebra with K₁(A) ≅ G and a unique tracial state, as constructed based on dimension drop algebras by Jiang and Su. First, we show that any two aperiodic elements in Aut(A)/WInn(A) are conjugate, where WInn(A) means the subgroup of Aut(A) consisting of automorphisms which are inner in the tracial representation.

In the second part of this paper, we consider a class of unital simple C*-algebras with a unique tracial state which contains the class of unital simple A𝕋-algebras of real rank zero with a unique tracial state. This class is closed under inductive limits and crossed products by actions of ℤ with the Rohlin property. Let A be a TAF-algebra in this class. We show that for any automorphism α of A there exists an automorphism ᾶ of A with the Rohlin property such that ᾶ and α are asymptotically unitarily equivalent. For the proof we use an aperiodic automorphism of the Jiang-Su algebra.

Let X be an irreducible smooth complex projective curve of genus g ≥ 4. Fix a line bundle L on X. Let M_Sp(L) be the moduli space of semistable symplectic bundles (E, φ : E ⊗ E → L) on X, with the symplectic form taking values in L. We show that the automorphism group of M_Sp(L) is generated by the automorphisms of the form E ↦ E ⊗ M, where , together with the automorphisms induced by automorphisms of X.

We find explicit projective models of a compact Shimura curve and of a (non-compact) surface which are the moduli spaces of principally polarized abelian fourfolds with an automorphism of order five. The surface has a 24-nodal canonical model in P⁴ which is the complete intersection of two S₅-invariant cubics. It is dominated by a Hilbert modular surface and we give a modular interpretation for this. We also determine the L-series of these varieties as well as those of several modular covers of the Shimura curve.

Glimm's theorem says that a UHF algebra is almost embedded in a separable C*-algebra not of type I. Applying his methods we obtain a covariant version of his result; a UHF algebra with a product type automorphism is covariantly embedded in such a C*-algebra equipped with an automorphism with full Connes spectrum.

In this paper, we discuss a relationship between the surface symmetry and the spectral asymmetry. More precisely we show that an automorphism of the Macbeath surface of genus 7, or one of the three Hurwitz surfaces of genus 14 is reducible if and only if the η-invariant of the corresponding mapping torus vanishes.

We introduce a notion of hyperbolicity and parabolicity for a holomorphic self-map $f:{\mathrm{\Delta }}^N\to {\mathrm{\Delta }}^N$ of the polydisc which does not admit fixed points in ${\mathrm{\Delta }}^N$. We generalize to the polydisc two classical one-variable results: we solve the Valiron equation for a hyperbolic $f$ and the Abel equation for a parabolic nonzero-step $f$. This is done by studying the canonical Kobayashi hyperbolic semi-model of $f$ and by obtaining a normal form for the automorphisms of the polydisc. In the case of the Valiron equation, we also describe the space of all solutions.

In this paper, we study the structure theory of two classes of Lie superalgebras ${𝒮}(q)$ of Block type, where $q$ is a positive integer. In particular, the automorphism groups, derivation superalgebras and central extensions of ${𝒮}(q)$ are completely determined.

By using the Bergman representative coordinates, we give the necessary and sufficient condition for the degree of automorphisms of quasi-circular domains fixing the origin to be bounded by the resonance order, thus solving a conjecture of the author.

Let $E_G$ be a holomorphic principal $G$-bundle on a compact connected Riemann surface $X$, where $G$ is a connected reductive complex affine algebraic group. Fix a finite subset $D\subset X$, and for each $x\in D$ fix $w_x\in \text{ad}{(E_G)}_x$. Let $T$ be a maximal torus in the group of all holomorphic automorphisms of $E_G$. We give a necessary and sufficient condition for the existence of a $T$-invariant logarithmic connection on $E_G$ singular over $D$ such that the residue over each $x\in D$ is $w_x$. We also give a necessary and sufficient condition for the existence of a logarithmic connection on $E_G$ singular over $D$ such that the residue over each $x\in D$ is $w_x$, under the assumption that each $w_x$ is $T$-rigid.

The automorphism group of a K3 surface with Picard number two is either the infinite cyclic group or the infinite dihedral group, if it is infinite. In this paper, we determine some conditions for a K3 surface of Picard number two to have the infinite dihedral automorphism group.

Let X be a full right Hilbert B-bimodule of finite type and be its generalized Cuntz algebra. We give a notion that the C*-algebra B is X-aperiodic. We show that the fixed point algebra ℱ_X for a gauge action is simple if and only if the C*-algebra B is X-aperiodic. For a invertible operator U on X with some properties, a quasi-free automorphism α_U of is defined. We give some conditions in order that α_U is inner in the case that B is X-aperiodic. We apply them to the automorphism α_U on Cuntz–Krieger algebras.

We construct some new matrix representations of Aut(F₃), the automorphism group of a free group of rank 3, and show that there are infinitely many distinct irreducible representations of Aut(F₃) in dimensions at most 42.

Let L be a finite-dimensional complex simple Lie algebra, L_ℤ be the ℤ-span of a Chevalley basis of L and L_R = R⊗_ℤL_ℤ be a Chevalley algebra of type L over a commutative ring R. Let be the nilpotent subalgebra of L_R spanned by the root vectors associated with positive roots. The aim of this paper is to determine the automorphism group of .

Let W(X) be a free commutative or a free associative algebra. The group of automorphisms of the semigroup End(W(X)) is studied.