arXiv subjects
Publications and source records attributed to Ryo Takahashi.
The main aim of this paper is to classify Ulrich ideals and Ulrich modules over two-dimensional Gorenstein rational singularities (rational double points) from a geometric point of view. To achieve this purpose, we introduce the notion of (weakly) special Cohen-Macaulay modules with respect to ideals, and study the relationship between those modules and Ulrich modules with respect to good ideals.
We propose a new seesaw model in an extra-dimensional setup where only right-handed neutrinos are bulk fields. In the model, localizations of an extra-dimensional wave function and brane Majorana mass of the right-handed neutrinos can be different among each generation of the right-handed neutrinos. The setup can lead to different suppression factor dependences of effective right-handed neutrino masses and neutrino Yukawa couplings for each generation. It is shown that the resultant mass spectra of the right-handed neutrinos and neutrino Yukawa couplings are favored in models of neutrino dark matter with baryogenesis.
We classify certain resolving subcategories of finitely generated modules over a commutative noetherian ring R by using integer-valued functions on Spec R. As an application we give a complete classification of resolving subcategories when R is a locally hypersurface ring. Our results also recover a "missing theorem" by Auslander.
The pressure-temperature phase diagram of an intermediate-valence compound YbPd was revealed via simultaneous ac-calorimetry and electrical resistivity measurements. Two successive structural phase transition temperatures, $T_1$ = 125 K and $T_2$ = 110 K, are found to decrease with increasing pressure. The magnetic ordering transition at $T_{\rm N} ~sim$ 1.9 K decreases monotonically up to 1.7 GPa and disappears discontinuously at $P_{\rm c} sim$ 1.9 GPa, where the structural phase transition at $T_2$ is also suppressed. At $P_{\rm c}$, enhancement of the effective mass and residual resistivity are observed. Another probable magnetic phase transition, however, is found to take place at $T_{\rm ML} sim$0.3 K and smoothly varies even when crossing $P_{\rm c}$. Structural phase transitions at ambient pressure were also studied by a single crystal X-ray diffraction measurement. Below $T_2$, a tetragonal lattice distortion with doubling of the unit cell along the c-axis is observed, and thus there are two inequivalent Yb-sites below $P_{\rm c}$. These results indicate that one Yb-site, having larger valence configuration and thus smaller Kondo temperature, orders at $T_{\rm N}$. The other phase transition at $T_{\rm ML}$ seems to couple to the crystal structure for $T_2 < T < T_1$. YbPd is a unique system exhibiting magnetic orderings in metallic charge-ordered Yb systems.
In this paper we study Ulrich ideals of and Ulrich modules over Cohen--Macaulay local rings from various points of view. We determine the structure of minimal free resolutions of Ulrich modules and their associated graded modules, and classify Ulrich ideals of numerical semigroup rings and rings of finite CM-representation type.
Let $R$ be a commutative Noetherian local ring. Assume that $R$ has a pair $\{x,y\}$ of exact zerodivisors such that $\dim R/(x,y)\ge2$ and all totally reflexive $R/(x)$-modules are free. We show that the first and second Brauer--Thrall type theorems hold for the category of totally reflexive $R$-modules. More precisely, we prove that, for infinitely many integers $n$, there exists an indecomposable totally reflexive $R$-module of multiplicity $n$. Moreover, if the residue field of $R$ is infinite, we prove that there exist infinitely many isomorphism classes of indecomposable totally reflexive $R$-modules of multiplicity $n$.
An x-ray diffraction study reveals the charge ordering structure in an intermediate valence magnet YbPd with a CsCl-structure. The valence of the Yb ions forms an incommensurate structure, characterized by the wavevector (+-0.07 +-0.07 1/2) below 130 K. At 105 K, the incommensurate structure turns into a commensurate structure, characterized by the wavevector (0 0 1/2). Based on the resonant x-ray diffraction spectra of the superlattice reflections, the valences of the Yb ions below 105 K are found to be 3+ and 2.6+. The origin of the long wavelength modulation is discussed with the aid of an Ising model having the second nearest neighbor interaction.
Motivated by a result of Araya, we extend the Auslander-Reiten duality theorem to Cohen-Macaulay local rings. We also study the Auslander-Reiten conjecture, which is rooted in Nakayama's work on finite dimensional algebras. One of our results detects a certain condition that forces the conjecture to hold over local rings of positive depth.
We study homological properties of test modules that are, in principle, modules that detect finite homological dimensions. The main outcome of our results is a generalization of a classical theorem of Auslander and Bridger: we prove that, if a commutative Noetherian complete local ring R admits a test module of finite Gorenstein dimension, then R is Gorenstein.
An origin of flavor mixings in quark and lepton sectors is still a mystery, and a structure of the flavor mixings in lepton sector seems completely different from that of quark sector. In this letter, we point out that the flavor mixing angles in quark and lepton sectors could be unified at a high energy scale, when neutrinos are degenerate. It means that a minimal flavor violation at a high energy scale can induce a rich variety of flavor mixings in quark and lepton sectors at a low energy scale through quantum corrections.
We investigate a possibility if a loop diagram via Higgsino can enhance the Higgs to diphoton decay width in supersymmetric models with an extension of Higgs sector. A model with an additional non-renormalizable term of Higgs fields is firstly analyzed where the higher order term can introduce the Higgs coupling to Higgsinos as well as charged Higgs bosons. We point out that a choice of the Higgs coupling to obtain a significant size of enhancement of diphoton decay width reduces the Higgs mass and/or a size of non-renormalizable term needs to be large and a cutoff scale is around the weak scale. Another model in which the Higgsino mass term is generated by a non-perturbative instanton effect via a strong dynamics in a context of SUSY QCD is also suggested. It is shown that the sign of the Higgs coupling to fermions is opposite from perturbative models due to an operator including bosonic fields in the denominator and a constructive contribution to the diphoton decay amplitude can be easily obtained in this kind of model.
We investigate a stability of leptonic self-complementarity such that sum of three mixing angles in lepton sector is 90 degrees. Renormalization group equations in a context of minimal supersymmetric standard model for the self-complementarity are analyzed. It is seen that one of Majorana phases plays an important role for the stability of self-complementarity. We find some stable solutions against quantum corrections at a low energy. An effective neutrino mass for neutrino-less double beta decay is also evaluated by the use of neutrino parameters giving rise to the stable solutions.
We present neutrino mass matrix textures in a minimal framework of the type-I seesaw mechanism where two right-handed Majorana neutrinos are introduced in order to reproduce experimental results of neutrino oscillations. The textures can lead to experimentally favored leptonic mixing angles described by the tri-bimaximal mixing with one additional rotation. We present minimal and next to minimal textures for the normal mass hierarchy case in a context of the texture zero. A minimal texture in the inverted hierarchy case is also constructed, which does not have any vanishing entries in a Dirac neutrino mass matrix. We also discuss some cases that model parameters in the textures are supposed to be a neutrino mass ratio and/or the Cabibbo angle. Predicted regions of mixing angles, a leptonic CP-violation parameter, and an effective mass for the neutrino-less double beta decay are presented in all textures.
Let R be a complete local hypersurface over an algebraically closed field of characteristic different from two, and suppose that R has countable Cohen-Macaulay representation type. In this paper, it is proved that the maximal Cohen-Macaulay R-modules which are locally free on the punctured spectrum are dominated by the maximal Cohen-Macaulay R-modules which are not locally free on the punctured spectrum. More precisely, there exists a single R-module X such that the indecomposable maximal Cohen-Macaulay R-modules not locally free on the punctured spectrum are X and its syzygy ΩX and that any other maximal Cohen-Macaulay R-module is obtained from some extension of X and ΩX.
This paper gives upper bounds for the dimension of the singularity category of a Cohen-Macaulay local ring with an isolated singularity. One of them recovers an upper bound given by Ballard, Favero and Katzarkov in the case of a hypersurface.
Let R be a Cohen-Macaulay local ring. Denote by mod R the category of finitely generated R-modules. In this paper, we consider the classification problem of resolving subcategories of mod R in terms of specialization-closed subsets of Spec R. We give a classification of the resolving subcategories closed under tensor products and transposes. Under restrictive hypotheses, we also give better classification results.
We study magnetic dipole moments of right-handed neutrinos in a keV neutrino dark matter model. This model is a simple extension of the standard model with only right-handed neutrinos and a pair of charged particles added. One of the right-handed neutrinos is the candidate of dark matter with a keV mass. Some bounds on the dark matter magnetic dipole moment and model parameters are obtained from cosmological observations.
We propose that a hierarchical spectrum of sterile neutrinos (eV, keV, $10^{13-15}$ GeV) is considered to as the explanations for MiniBooNE and LSND oscillation anomalies, dark matter, and baryon asymmetry of the universe (BAU) respectively. The scenario can also realize the smallness of active neutrino masses by seesaw mechanism.