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Affine Nijenhuis Operators and Hochschild Cohomology of Trusses 桁架的仿射Nijenhuis算子和Hochschild上同调
IF 0.9 3区 物理与天体物理
Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-03-22 DOI: 10.3842/SIGMA.2023.056
Tomasz Brzezi'nski, J. Papworth
{"title":"Affine Nijenhuis Operators and Hochschild Cohomology of Trusses","authors":"Tomasz Brzezi'nski, J. Papworth","doi":"10.3842/SIGMA.2023.056","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.056","url":null,"abstract":"The classical Hochschild cohomology theory of rings is extended to abelian heaps with distributing multiplication or trusses. This cohomology is then employed to give necessary and sufficient conditions for a Nijenhuis product on a truss (defined by the extension of the Nijenhuis product on an associative ring introduced by Carinena, Grabowski and Marmo in [Internat. J. Modern Phys. A 15 (2000), 4797-4810, arXiv:math-ph/0610011]) to be associative. The definition of Nijenhuis product and operators on trusses is then linearised to the case of affine spaces with compatible associative multiplications or associative affgebras. It is shown that this construction leads to compatible Lie brackets on an affine space.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48870075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Modified Green-Hyperbolic Operators 改进的绿色-双曲算子
IF 0.9 3区 物理与天体物理
Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-03-06 DOI: 10.3842/SIGMA.2023.057
C. Fewster
{"title":"Modified Green-Hyperbolic Operators","authors":"C. Fewster","doi":"10.3842/SIGMA.2023.057","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.057","url":null,"abstract":"Green-hyperbolic operators - partial differential operators on globally hyperbolic spacetimes that (together with their formal duals) possess advanced and retarded Green operators - play an important role in many areas of mathematical physics. Here, we study modifications of Green-hyperbolic operators by the addition of a possibly nonlocal operator acting within a compact subset $K$ of spacetime, and seek corresponding '$K$-nonlocal' generalised Green operators. Assuming the modification depends holomorphically on a parameter, conditions are given under which $K$-nonlocal Green operators exist for all parameter values, with the possible exception of a discrete set. The exceptional points occur precisely where the modified operator admits nontrivial smooth homogeneous solutions that have past- or future-compact support. Fredholm theory is used to relate the dimensions of these spaces to those corresponding to the formal dual operator, switching the roles of future and past. The $K$-nonlocal Green operators are shown to depend holomorphically on the parameter in the topology of bounded convergence on maps between suitable Sobolev spaces, or between suitable spaces of smooth functions. An application to the LU factorisation of systems of equations is described.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45864735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Asymptotic Structure of the Centred Hyperbolic 2-Monopole Moduli Space 中心双曲2-单极模空间的渐近结构
IF 0.9 3区 物理与天体物理
Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-02-27 DOI: 10.3842/SIGMA.2023.043
G. Franchetti, C. Ross
{"title":"The Asymptotic Structure of the Centred Hyperbolic 2-Monopole Moduli Space","authors":"G. Franchetti, C. Ross","doi":"10.3842/SIGMA.2023.043","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.043","url":null,"abstract":"We construct an asymptotic metric on the moduli space of two centred hyperbolic monopoles by working in the point particle approximation, that is treating well-separated monopoles as point particles with an electric, magnetic and scalar charge and re-interpreting the dynamics of the 2-particle system as geodesic motion with respect to some metric. The corresponding analysis in the Euclidean case famously yields the negative mass Taub-NUT metric, which asymptotically approximates the L2 metric on the moduli space of two Euclidean monopoles, the Atiyah-Hitchin metric. An important difference with the Euclidean case is that, due to the absence of Galilean symmetry, in the hyperbolic case it is not possible to factor out the centre of mass motion. Nevertheless we show that we can consistently restrict to a 3-dimensional configuration space by considering antipodal configurations. In complete parallel with the Euclidean case, the metric that we obtain is then the hyperbolic analogue of negative mass Taub-NUT. We also show how the metric obtained is related to the asymptotic form of a hyperbolic analogue of the Atiyah-Hitchin metric constructed by Hitchin.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43005447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Yamabe Invariants, Homogeneous Spaces, and Rational Complex Surfaces Yamabe不变量、齐次空间和有理复曲面
IF 0.9 3区 物理与天体物理
Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-02-23 DOI: 10.3842/SIGMA.2023.027
C. LeBrun
{"title":"Yamabe Invariants, Homogeneous Spaces, and Rational Complex Surfaces","authors":"C. LeBrun","doi":"10.3842/SIGMA.2023.027","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.027","url":null,"abstract":"The Yamabe invariant is a diffeomorphism invariant of smooth compact manifolds that arises from the normalized Einstein-Hilbert functional. This article highlights the manner in which one compelling open problem regarding the Yamabe invariant appears to be closely tied to static potentials and the first eigenvalue of the Laplacian.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42760070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ten Compatible Poisson Brackets on $mathbb P^5$ $mathbb P^5上的十个兼容泊松括号$
IF 0.9 3区 物理与天体物理
Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-01-31 DOI: 10.3842/SIGMA.2023.059
Ville Nordstrom, A. Polishchuk
{"title":"Ten Compatible Poisson Brackets on $mathbb P^5$","authors":"Ville Nordstrom, A. Polishchuk","doi":"10.3842/SIGMA.2023.059","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.059","url":null,"abstract":"We give explicit formulas for ten compatible Poisson brackets on $mathbb P^5$ found in arXiv:2007.12351.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47497627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solitons in the Gauged Skyrme-Maxwell Model 测量的斯基姆-麦克斯韦模型中的孤子
IF 0.9 3区 物理与天体物理
Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-01-30 DOI: 10.3842/SIGMA.2023.042
L. R. Livramento, E. Radu, Y. Shnir
{"title":"Solitons in the Gauged Skyrme-Maxwell Model","authors":"L. R. Livramento, E. Radu, Y. Shnir","doi":"10.3842/SIGMA.2023.042","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.042","url":null,"abstract":"We consider soliton solutions of the U(1) gauged Skyrme model with the pion mass term. The domain of existence of gauged Skyrmions is restricted from above by the value of the pion mass. Concentrating on the solutions of topological degree one, we find that coupling to the electromagnetic field breaks the symmetry of the configurations, the Skyrmions carrying both an electric charge and a magnetic flux, with an induced dipole magnetic moment. The Skyrmions also possess an angular momentum, which is quantized in the units of the electric charge. The mass of the gauged Skyrmions monotonically decreases with increase of the gauge coupling.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47374385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the Spectrum of Certain Hadamard Manifolds 关于某些哈达玛流形的谱
IF 0.9 3区 物理与天体物理
Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-01-26 DOI: 10.3842/SIGMA.2023.050
W. Ballmann, Mayukh Mukherjee, Panagiotis Polymerakis
{"title":"On the Spectrum of Certain Hadamard Manifolds","authors":"W. Ballmann, Mayukh Mukherjee, Panagiotis Polymerakis","doi":"10.3842/SIGMA.2023.050","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.050","url":null,"abstract":"We show the absolute continuity of the spectrum and determine the spectrum as a set for two classes of Hadamard manifolds and for specific domains and quotients of one of the classes.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44941314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class c类次极大对称向量常微分方程的唯一性
IF 0.9 3区 物理与天体物理
Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-01-23 DOI: 10.3842/SIGMA.2023.058
Johnson Allen Kessy, D. The
{"title":"On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class","authors":"Johnson Allen Kessy, D. The","doi":"10.3842/SIGMA.2023.058","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.058","url":null,"abstract":"The fundamental invariants for vector ODEs of order $ge 3$ considered up to point transformations consist of generalized Wilczynski invariants and C-class invariants. An ODE of C-class is characterized by the vanishing of the former. For any fixed C-class invariant ${mathcal U}$, we give a local (point) classification for all submaximally symmetric ODEs of C-class with ${mathcal U} not equiv 0$ and all remaining C-class invariants vanishing identically. Our results yield generalizations of a well-known classical result for scalar ODEs due to Sophus Lie. Fundamental invariants correspond to the harmonic curvature of the associated Cartan geometry. A key new ingredient underlying our classification results is an advance concerning the harmonic theory associated with the structure of vector ODEs of C-class. Namely, for each irreducible C-class module, we provide an explicit identification of a lowest weight vector as a harmonic 2-cochain.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48633886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spinh Manifolds Spinh集合管
IF 0.9 3区 物理与天体物理
Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-01-23 DOI: 10.3842/SIGMA.2023.012
H. B. Lawson
{"title":"Spinh Manifolds","authors":"H. B. Lawson","doi":"10.3842/SIGMA.2023.012","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.012","url":null,"abstract":"The concept of a Spinh-manifold, which is a cousin of Spin- and Spinc-manifolds, has been at the center of much research in recent years. This article discusses some of the highlights of this story.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46481310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Koenigs Theorem and Superintegrable Liouville Metrics Koenigs定理与超积分Liouville度量
IF 0.9 3区 物理与天体物理
Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-01-22 DOI: 10.3842/SIGMA.2023.048
G. Valent
{"title":"Koenigs Theorem and Superintegrable Liouville Metrics","authors":"G. Valent","doi":"10.3842/SIGMA.2023.048","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.048","url":null,"abstract":"In a first part, we give a new proof of Koenigs theorem and, in a second part, we determine the local form of all the superintegrable Riemannian Liouville metrics as well as their global geometries.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44584781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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