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Journal articles on the topic 'Compact homogenous spaces'

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Author: Grafiati

Published: 10 March 2023

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1

Golasiński, Marek. "On homotopy nilpotency." Glasnik Matematicki 56, no. 2 (December 23, 2021): 391–406. http://dx.doi.org/10.3336/gm.56.2.10.

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We review established and recent results on the homotopy nilpotence of spaces. In particular, the homotopy nilpotency of the loop spaces \(\Omega(G/K)\) of homogenous spaces \(G/K\) for a compact Lie group \(G\) and its closed homotopy nilpotent subgroup \(K \lt G\) is discussed.

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2

Abbas, Fadhil, and Hassan A. Alhayo. "Fuzzy ideal topological vector spaces." Mathematica Slovaca 72, no. 4 (August 1, 2021): 993–1000. http://dx.doi.org/10.1515/ms-2022-0069.

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Abstract In this paper, we introduce the concept of fuzzy ideal topological vector spaces and study the basic properties of fuzzy-I-open and fuzzy-I-closed sets in fuzzy ideal topological vector spaces. Also, we study the properties of fuzzy-I-Hausdorff and fuzzy-I-compact in fuzzy ideal topological vector spaces. Furthermore, we introduce the concepts of fuzzy-I-homogenous space, fuzzy-I-monomorphism space, fuzzy-I-isomorphism space and fuzzy-I-automorphism space. Finally, we introduce the concepts of fuzzy-I-bounded set, fuzzy-I-balanced set, fuzzy-I-symmetric set and study their properties in fuzzy ideal topological vector spaces.

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3

Rejali, Ali, and Navid Sabzali. "On the homological and algebraical properties of some Feichtinger algebras." Mathematica Slovaca 71, no. 5 (October 1, 2021): 1211–28. http://dx.doi.org/10.1515/ms-2021-0049.

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Abstract Let G be a locally compact group (not necessarily abelian) and B be a homogeneous Banach space on G, which is in a good situation with respect to a homogeneous function algebra on G. Feichtinger showed that there exists a minimal Banach space B min in the family of all homogenous Banach spaces C on G, containing all elements of B with compact support. In this paper, the amenability and super amenability of B min with respect to the convolution product or with respect to the pointwise product are showed to correspond to amenability, discreteness or finiteness of the group G and conversely. We also prove among other things that B min is a symmetric Segal subalgebra of L 1(G) on an IN-group G, under certain conditions, and we apply our results to study pseudo-amenability and some other homological properties of B min on IN-groups. Furthermore, we determine necessary and sufficient conditions on A under which A min $\mathcal{A}_{\min}$ with the pointwise product is an abstract Segal algebra or Segal algebra in A, whenever A is a homogeneous function algebra with an approximate identity. We apply these results to study amenability of some Feichtinger algebras with respect to the pointwise product.

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4

Rejali, Ali, and Navid Sabzali. "On the homological and algebraical properties of some Feichtinger algebras." Mathematica Slovaca 71, no. 5 (October 1, 2021): 1211–28. http://dx.doi.org/10.1515/ms-2021-0049.

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Abstract Let G be a locally compact group (not necessarily abelian) and B be a homogeneous Banach space on G, which is in a good situation with respect to a homogeneous function algebra on G. Feichtinger showed that there exists a minimal Banach space B min in the family of all homogenous Banach spaces C on G, containing all elements of B with compact support. In this paper, the amenability and super amenability of B min with respect to the convolution product or with respect to the pointwise product are showed to correspond to amenability, discreteness or finiteness of the group G and conversely. We also prove among other things that B min is a symmetric Segal subalgebra of L 1(G) on an IN-group G, under certain conditions, and we apply our results to study pseudo-amenability and some other homological properties of B min on IN-groups. Furthermore, we determine necessary and sufficient conditions on A under which A min $\mathcal{A}_{\min}$ with the pointwise product is an abstract Segal algebra or Segal algebra in A, whenever A is a homogeneous function algebra with an approximate identity. We apply these results to study amenability of some Feichtinger algebras with respect to the pointwise product.

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5

Ghaani Farashahi, Arash. "A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups." Canadian Journal of Mathematics 70, no. 1 (February 1, 2018): 97–116. http://dx.doi.org/10.4153/cjm-2016-043-9.

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AbstractThis paper introduces a class of abstract linear representations on Banach convolution function algebras over homogeneous spaces of compact groups. LetGbe a compact group andHa closed subgroup ofG. Letμbe the normalizedG-invariant measure over the compact homogeneous spaceG/Hassociated with Weil's formula and. We then present a structured class of abstract linear representations of the Banach convolution function algebrasLp(G/H,μ).

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6

Nikiel, J., and E. D. Tymchatyn. "On Homogeneous Images of Compact Ordered Spaces." Canadian Journal of Mathematics 45, no. 2 (April 1, 1993): 380–93. http://dx.doi.org/10.4153/cjm-1993-019-7.

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AbstractWe answer a 1975 question of G R Gordh by showing that if X is a homogeneous compactum which is the continuous image of a compact ordered space then at least one of the following holds(I) X is metrizable, (II) dim X = 0 or (III) X is a union of finitely many pairwise disjoint generalized simple closed curves.We begin to examine the structure of homogeneous 0-dimensional spaces which are continuous images of ordered compacta.

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7

Berestovskii, V. N., and Y. G. Nikonorov. "О конечных однородных метрических пространствах." Владикавказский математический журнал, no. 2 (June 22, 2022): 51–61. http://dx.doi.org/10.46698/h7670-4977-9928-z.

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This survey is devoted to recently obtained results on finite homogeneousmetric spaces. The main subject of discussion is the classification of regular and semiregular polytopes in Euclidean spacesby whether or not their vertex sets have the normal homogeneity property or the Clifford - Wolf homogeneity property.Every finite homogeneous metric subspace of an Euclidean space represents the vertex set of a compact convex polytope with the isometry group that is transitive on the set of vertices, moreover, all these vertices lie on some sphere. Consequently, the study of such subsets is closely related to the theory of convex polytopes in Euclidean spaces. The normal generalized homogeneity and the Clifford - Wolf homogeneity describe more stronger properties than the homogeneity. Therefore, it is natural to first check the presence of these properties for the vertex sets of regular and semiregular polytopes. In addition to the classification results, the paper contains a description of the main tools for the study of the relevant objects.

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8

Ikawa, Osamu. "Equivariant minimal immersions of compact Riemannian homogeneous spaces into compact Riemannian homogeneous spaces." Tsukuba Journal of Mathematics 17, no. 1 (June 1993): 169–88. http://dx.doi.org/10.21099/tkbjm/1496162138.

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9

Gorbachev, Dmitry Viktorovich. "Nikol’skii constants for compact homogeneous spaces." Chebyshevskii sbornik 22, no. 4 (2021): 99–112. http://dx.doi.org/10.22405/2226-8383-2021-22-4-99-112.

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10

Gorbatsevich, V. V. "Stable cohomology of compact homogeneous spaces." Mathematical Notes 83, no. 5-6 (June 2008): 735–43. http://dx.doi.org/10.1134/s0001434608050192.

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11

Gorbatsevich, V. V. "Invariant distributions on compact homogeneous spaces." Sbornik: Mathematics 204, no. 12 (December 31, 2013): 1712–27. http://dx.doi.org/10.1070/sm2013v204n12abeh004357.

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12

Gorbatsevich, V. V. "Compact homogeneous spaces and their generalizations." Journal of Mathematical Sciences 153, no. 6 (September 2008): 763–98. http://dx.doi.org/10.1007/s10958-008-9145-9.

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13

Weiss, Barak. "Unique ergodicity on compact homogeneous spaces." Proceedings of the American Mathematical Society 129, no. 2 (August 28, 2000): 585–92. http://dx.doi.org/10.1090/s0002-9939-00-05791-9.

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14

BISWAS, INDRANIL, and PRALAY CHATTERJEE. "SECOND COHOMOLOGY OF COMPACT HOMOGENEOUS SPACES." International Journal of Mathematics 24, no. 09 (August 2013): 1350076. http://dx.doi.org/10.1142/s0129167x13500766.

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In Theorem 3.3 of [I. Biswas and P. Chatterjee, On the exactness of Kostant–Kirillov form and the second cohomology of nilpotent orbits, Int. J. Math.23(8) (2012)], the second cohomology of a quotient of a compact semisimple real Lie group was computed. In this addendum to the above paper, we give a simple topological proof of this theorem.

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15

Parthasarathy, K., and N. Shravan Kumar. "Feichtinger's Segal algebra on homogeneous spaces." International Journal of Mathematics 26, no. 08 (July 2015): 1550054. http://dx.doi.org/10.1142/s0129167x15500548.

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Let K be a compact subgroup of a locally compact group G. We extend to the context of homogeneous spaces, G/K, the definition of Feichtinger's Segal algebra. The functorial properties of the Segal algebra are proved.

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16

Van, LeHong. "Globally minimal homogeneous subspaces in compact homogeneous sympletic spaces." Acta Applicandae Mathematicae 24, no. 3 (September 1991): 275–308. http://dx.doi.org/10.1007/bf00047047.

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17

Wilson, Mitsuru. "Connes-Landi spheres are homogeneous spaces." Revista Colombiana de Matemáticas 53, supl (December 11, 2019): 257–71. http://dx.doi.org/10.15446/recolma.v53nsupl.84099.

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In this paper, we review some recent developments of compact quantum groups that arise as θ-deformations of compact Lie groups of rank at least two. A θ-deformation is merely a 2-cocycle deformation using an action of a torus of dimension higher than 2. Using the formula (Lemma 5.3) developed in [11], we derive the noncommutative 7-sphere in the sense of Connes and Landi [3] as the fixed-point subalgebra.

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18

Carroy, Raphaël, Andrea Medini, and Sandra Müller. "Every zero-dimensional homogeneous space is strongly homogeneous under determinacy." Journal of Mathematical Logic 20, no. 03 (March 4, 2020): 2050015. http://dx.doi.org/10.1142/s0219061320500154.

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All spaces are assumed to be separable and metrizable. We show that, assuming the Axiom of Determinacy, every zero-dimensional homogeneous space is strongly homogeneous (i.e. all its non-empty clopen subspaces are homeomorphic), with the trivial exception of locally compact spaces. In fact, we obtain a more general result on the uniqueness of zero-dimensional homogeneous spaces which generate a given Wadge class. This extends work of van Engelen (who obtained the corresponding results for Borel spaces), complements a result of van Douwen, and gives partial answers to questions of Terada and Medvedev.

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19

Gorbatsevich, Vladimir Vital'evich. "On stationary subgroups of compact homogeneous spaces." Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, no. 4 (2019): 36–51. http://dx.doi.org/10.26907/0021-3446-2019-4-36-51.

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20

Gorbatsevich, V. V. "On stationary subgroups of compact homogeneous spaces." Russian Mathematics 63, no. 4 (April 2019): 31–43. http://dx.doi.org/10.3103/s1066369x19040042.

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21

Huang, Jing-Song. "Harmonic analysis on compact polar homogeneous spaces." Pacific Journal of Mathematics 175, no. 2 (October 1, 1996): 553–69. http://dx.doi.org/10.2140/pjm.1996.175.553.

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22

Gorbatsevich, V. V. "The automorphism groups of compact homogeneous spaces." Siberian Mathematical Journal 57, no. 4 (July 2016): 565–81. http://dx.doi.org/10.1134/s0037446616040017.

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23

Bramati, Roberto. "Brascamp–Lieb Inequalities on Compact Homogeneous Spaces." Analysis and Geometry in Metric Spaces 7, no. 1 (January 1, 2019): 130–57. http://dx.doi.org/10.1515/agms-2019-0007.

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Abstract We provide a general strategy to construct multilinear inequalities of Brascamp–Lieb type on compact homogeneous spaces of Lie groups. As an application we obtain sharp integral inequalities on the real unit sphere involving functions with some degree of symmetry.

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24

Gorbatsevich, V. V. "Sub-Riemannian geometries on compact homogeneous spaces." Izvestiya: Mathematics 78, no. 3 (June 25, 2014): 459–74. http://dx.doi.org/10.1070/im2014v078n03abeh002694.

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25

Ugulava, Duglas. "Approximation in mean on homogeneous compact spaces." Transactions of A. Razmadze Mathematical Institute 171, no. 2 (August 2017): 231–37. http://dx.doi.org/10.1016/j.trmi.2017.02.003.

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26

Panelli, Francesco, and Fabio Podestà. "Hermitian Curvature Flow on Compact Homogeneous Spaces." Journal of Geometric Analysis 30, no. 4 (July 16, 2019): 4193–210. http://dx.doi.org/10.1007/s12220-019-00239-7.

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27

Dreseler, Bernd. "Hardy's inequality for certain compact homogeneous spaces." Archiv der Mathematik 45, no. 4 (October 1985): 359–65. http://dx.doi.org/10.1007/bf01198240.

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28

Ohno, Shinji, Takashi Sakai, and Hajime Urakawa. "Biharmonic homogeneous hypersurfaces in compact symmetric spaces." Differential Geometry and its Applications 43 (December 2015): 155–79. http://dx.doi.org/10.1016/j.difgeo.2015.09.005.

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29

Ebert, Svend, and Jens Wirth. "Diffusive wavelets on groups and homogeneous spaces." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 3 (June 2011): 497–520. http://dx.doi.org/10.1017/s030821051000051x.

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We explain the basic ideas behind the concept of diffusive wavelets on spheres in the language of representation theory of Lie groups and within the framework of the group Fourier transform given by the Peter-Weyl decomposition of L2() for a compact Lie group . After developing a general concept for compact groups and their homogeneous spaces, we give concrete examples for tori, which reflect the situation on ℝn, and for 2 and 3 spheres.

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30

Mirotin, Adolf R. "Hausdorff operators on homogeneous spaces of locally compact groups." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (July 30, 2020): 28–35. http://dx.doi.org/10.33581/2520-6508-2020-2-28-35.

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Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author since 2019. The purpose of this paper is to define and study Hausdorff operators on Lebesgue and real Hardy spaces over homogeneous spaces of locally compact groups. We introduce in particular an atomic Hardy space over homogeneous spaces of locally compact groups and obtain conditions for boundedness of Hausdorff operators on such spaces. Several corollaries are considered and unsolved problems are formulated.

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31

Tralle, Aleksy. "On Formality of Some Homogeneous Spaces." Symmetry 11, no. 8 (August 5, 2019): 1011. http://dx.doi.org/10.3390/sym11081011.

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Let G / H be a homogeneous space of a compact simple classical Lie group G. Assume that the maximal torus T H of H is conjugate to a torus T β whose Lie algebra t β is the kernel of the maximal root β of the root system of the complexified Lie algebra g c . We prove that such homogeneous space is formal. As an application, we give a short direct proof of the formality property of compact homogeneous 3-Sasakian spaces of classical type. This is a complement to the work of Fernández, Muñoz, and Sanchez which contains a full analysis of the formality property of S O ( 3 ) -bundles over the Wolf spaces and the proof of the formality property of homogeneous 3-Sasakian manifolds as a corollary.

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32

Tojo, Koichi. "Obstructions to the existence of compact Clifford–Klein forms for tangential symmetric spaces." International Journal of Mathematics 32, no. 10 (July 29, 2021): 2150074. http://dx.doi.org/10.1142/s0129167x21500749.

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For a homogeneous space [Formula: see text] of reductive type, we consider the tangential homogeneous space [Formula: see text]. In this paper, we give obstructions to the existence of compact Clifford–Klein forms for such tangential symmetric spaces and obtain new tangential symmetric spaces which do not admit compact Clifford–Klein forms. As a result, in the class of irreducible classical semisimple symmetric spaces, we have only two types of symmetric spaces which are not proved not to admit compact Clifford–Klein forms. The existence problem of compact Clifford–Klein forms for homogeneous spaces of reductive type, which was initiated by Kobayashi in 1980s, has been studied by various methods but is not completely solved yet. On the other hand, the one for tangential homogeneous spaces has been studied since 2000s and an analogous criterion was proved by Kobayashi and Yoshino. In concrete examples, further works are needed to verify Kobayashi–Yoshino’s condition by direct calculations. In this paper, some easy-to-check necessary conditions ([Formula: see text][Formula: see text]obstructions) for the existence of compact quotients in the tangential setting are given, and they are applied to the case of symmetric spaces. The conditions are related to various fields of mathematics such as associated pair of symmetric space, Calabi–Markus phenomenon, trivializability of vector bundle (parallelizability, Pontrjagin class), Hurwitz–Radon number and Pfister’s theorem (the existence problem of common zero points of polynomials of odd degree).

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33

Ohno, Shinji, Takashi Sakai, and Hajime Urakawa. "Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups." Hiroshima Mathematical Journal 49, no. 1 (March 2019): 47–115. http://dx.doi.org/10.32917/hmj/1554516038.

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34

Hrušák, Michael, and Jan van Mill. "Nearly Countable Dense Homogeneous Spaces." Canadian Journal of Mathematics 66, no. 4 (August 1, 2014): 743–58. http://dx.doi.org/10.4153/cjm-2013-006-8.

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AbstractWe study separable metric spaces with few types of countable dense sets. We present a structure theorem for locally compact spaces having precisely n types of countable dense sets: such a space contains a subset S of size at most n−1 such that S is invariant under all homeomorphisms of X and X ∖ S is countable dense homogeneous. We prove that every Borel space having fewer than c types of countable dense sets is Polish. The natural question of whether every Polish space has either countably many or c many types of countable dense sets is shown to be closely related to Topological Vaught's Conjecture.

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35

Onneweer, C., and Su Weiyi. "Homogeneous Besov spaces on locally compact Vilenkin groups." Studia Mathematica 93, no. 1 (1989): 17–39. http://dx.doi.org/10.4064/sm-93-1-17-39.

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36

Gichev, V. "Invariant Function Algebras on Compact Commutative Homogeneous Spaces." Moscow Mathematical Journal 8, no. 4 (2008): 697–709. http://dx.doi.org/10.17323/1609-4514-2008-8-4-697-709.

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37

Guan, Daniel. "Toward a classification of compact complex homogeneous spaces." Journal of Algebra 273, no. 1 (March 2004): 33–59. http://dx.doi.org/10.1016/j.jalgebra.2003.11.007.

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38

Günther, Felix. "The local geometry of compact homogeneous Lorentz spaces." Journal of Geometry and Physics 89 (March 2015): 60–73. http://dx.doi.org/10.1016/j.geomphys.2014.12.007.

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39

Blümlinger, M., M. Drmota, and R. F. Tichy. "Asymptotic distribution of functions on compact homogeneous spaces." Annali di Matematica Pura ed Applicata 152, no. 1 (December 1988): 79–93. http://dx.doi.org/10.1007/bf01766142.

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40

Kath, I. "Pseudo-RiemannianT-duals of compact Riemannian homogeneous spaces." Transformation Groups 5, no. 2 (June 2000): 157–79. http://dx.doi.org/10.1007/bf01236467.

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41

Gigante, Giuliana. "Hyperbolicity outside a compact set and homogeneous spaces." Annali di Matematica Pura ed Applicata 176, no. 1 (December 1999): 73–93. http://dx.doi.org/10.1007/bf02505990.

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42

Hauschild, Volker. "Actions of compact Lie groups on homogeneous spaces." Mathematische Zeitschrift 189, no. 4 (December 1985): 475–86. http://dx.doi.org/10.1007/bf01168154.

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43

Malyshev, F. M. "Compact complex homogeneous spaces with finite fundamental group." Journal of Soviet Mathematics 31, no. 5 (December 1985): 3235–37. http://dx.doi.org/10.1007/bf02105143.

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44

Shchetinin, Alexander. "On a class of compact homogeneous spaces I." Annals of Global Analysis and Geometry 6, no. 2 (1988): 119–40. http://dx.doi.org/10.1007/bf00133035.

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45

Ichikawa, Kei, and Tomonori Noda. "Instability for harmonic foliations on compact homogeneous spaces." Differential Geometry and its Applications 27, no. 1 (February 2009): 119–23. http://dx.doi.org/10.1016/j.difgeo.2008.06.012.

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46

Shchetinin, Alexander. "On a class of compact homogeneous spaces II." Annals of Global Analysis and Geometry 8, no. 3 (1990): 227–47. http://dx.doi.org/10.1007/bf00127937.

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47

ESMAEELZADEH, F., R. A. KAMYABI GOL, and R. RAISI TOUSI. "ON THE CONTINUOUS WAVELET TRANSFORM ON HOMOGENEOUS SPACES." International Journal of Wavelets, Multiresolution and Information Processing 10, no. 04 (July 2012): 1250038. http://dx.doi.org/10.1142/s0219691312500385.

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Let G be a locally compact group with a compact subgroup H. We define a square integrable representation of a homogeneous space G/H on a Hilbert space [Formula: see text]. The reconstruction formula for G/H is established and as a result it is concluded that the set of admissible vectors is path connected. The continuous wavelet transform on G/H is defined and it is shown that the range of the continuous wavelet transform is a reproducing kernel Hilbert space. Moreover, we obtain a necessary and sufficient condition for the continuous wavelet transform to be onto.

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48

Lauret, Jorge, and Cynthia E. Will. "Prescribing Ricci curvature on homogeneous spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2022, no. 783 (January 6, 2022): 95–133. http://dx.doi.org/10.1515/crelle-2021-0069.

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Abstract The prescribed Ricci curvature problem in the context of G-invariant metrics on a homogeneous space M = G / K {M=G/K} is studied. We focus on the metrics at which the map g ↦ Rc ⁡ ( g ) {g\mapsto\operatorname{Rc}(g)} is, locally, as injective and surjective as it can be. Our main result is that such property is generic in the compact case. Our main tool is a formula for the Lichnerowicz Laplacian we prove in terms of the moment map for the variety of algebras.

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49

Ghaani Farashahi, Arash. "Abstract measure algebras over homogeneous spaces of compact groups." International Journal of Mathematics 29, no. 01 (January 2018): 1850005. http://dx.doi.org/10.1142/s0129167x18500052.

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This paper presents a systematic study for abstract Banach measure algebras over homogeneous spaces of compact groups. Let [Formula: see text] be a closed subgroup of a compact group [Formula: see text] and [Formula: see text] be the left coset space associated to the subgroup [Formula: see text] in [Formula: see text]. Also, let [Formula: see text] be the Banach measure space consists of all complex measures over [Formula: see text]. Then we introduce the abstract notions of convolution and involution over the Banach measure space [Formula: see text].

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50

Gorbatsevich, V. V. "Compact homogeneous spaces of reductive Lie groups and spaces close to them." Sbornik: Mathematics 207, no. 3 (March 31, 2016): 342–57. http://dx.doi.org/10.1070/sm8487.

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