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Journal articles on the topic 'Compact groups'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 July 2024

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1

Hofmann, Karl Heinrich, and Sidney A. Morris. "Free compact groups I: Free compact abelian groups." Topology and its Applications 23, no. 1 (June 1986): 41–64. http://dx.doi.org/10.1016/0166-8641(86)90016-7.

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2

Hofmann, Karl Heinrich, and Sidney A. Morris. "Free compact groups I: Free compact abelian groups." Topology and its Applications 28, no. 1 (February 1988): 101–2. http://dx.doi.org/10.1016/0166-8641(88)90040-5.

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3

Tovmassian, H. M., and V. H. Chavushyan. "Compact Groups: Local Groups?" Astronomical Journal 119, no. 4 (April 2000): 1687–90. http://dx.doi.org/10.1086/301296.

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4

Arhangel'skiǐ, A. V. "On countably compact topologies on compact groups and on dyadic compacta." Topology and its Applications 57, no. 2-3 (May 1994): 163–81. http://dx.doi.org/10.1016/0166-8641(94)90048-5.

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5

Hofmann, Karl H., and Christian Terp. "Compact subgroups of Lie groups and locally compact groups." Proceedings of the American Mathematical Society 120, no. 2 (February 1, 1994): 623. http://dx.doi.org/10.1090/s0002-9939-1994-1166357-9.

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6

Bagley, R. W., T. S. Wu, and J. S. Yang. "Locally compact groups: maximal compact subgroups and N-groups." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 1 (July 1988): 47–64. http://dx.doi.org/10.1017/s0305004100065233.

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AbstractIf G is a locally compact group such thatG/G0contains a uniform compactly generated nilpotent subgroup, thenGhas a maximal compact normal subgroupKsuch thatG/Gis a Lie group. A topological groupGis an N-group if, for each neighbourhoodUof the identity and each compact setC⊂G, there is a neighbourhoodVof the identity such thatfor eachg∈G. Several results on N-groups are obtained and it is shown that a related weaker condition is equivalent to local finiteness for certain totally disconnected groups.

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7

Priwitzer, Barbara. "Compact groups on compact projective planes." Geometriae Dedicata 58, no. 3 (December 1995): 245–58. http://dx.doi.org/10.1007/bf01263456.

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8

ENOCHS, EDGAR E., J. R. GARCÍA ROZAS, LUIS OYONARTE, and OVERTOUN M. G. JENDA. "Compact coGalois groups." Mathematical Proceedings of the Cambridge Philosophical Society 128, no. 2 (March 2000): 233–44. http://dx.doi.org/10.1017/s0305004199004156.

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9

Fay, Temple H., and Gary L. Walls. "Compact nilpotent groups." Communications in Algebra 17, no. 9 (January 1989): 2255–68. http://dx.doi.org/10.1080/00927878908823846.

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10

Melleray, Julien. "Compact metrizable groups are isometry groups of compact metric spaces." Proceedings of the American Mathematical Society 136, no. 04 (December 28, 2007): 1451–55. http://dx.doi.org/10.1090/s0002-9939-07-08727-8.

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11

Kalantar, Mehrdad, and Matthias Neufang. "From Quantum Groups to Groups." Canadian Journal of Mathematics 65, no. 5 (October 1, 2013): 1073–94. http://dx.doi.org/10.4153/cjm-2012-047-x.

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AbstractIn this paper we use the recent developments in the representation theory of locally compact quantum groups, to assign to each locally compact quantum group 𝔾 a locally compact group 𝔾˜ that is the quantum version of point-masses and is an invariant for the latter. We show that “quantum point-masses” can be identified with several other locally compact groups that can be naturally assigned to the quantum group 𝔾. This assignment preserves compactness as well as discreteness (hence also finiteness), and for large classes of quantum groups, amenability. We calculate this invariant for some of the most well-known examples of non-classical quantum groups. Also, we show that several structural properties of 𝔾 are encoded by 𝔾˜; the latter, despite being a simpler object, can carry very important information about 𝔾.

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12

Mirotin, A. "Compact Hankel operators on compact Abelian groups." St. Petersburg Mathematical Journal 33, no. 3 (May 5, 2022): 569–84. http://dx.doi.org/10.1090/spmj/1715.

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The classical theorems of Kronecker, Hartman, Peller, and Adamyan–Arov–Krein are extended to the context of a connected compact Abelian group G G with linearly ordered group of characters, on the basis of a description of the structure of compact Hankel operators on G G . Beurling’s theorem on invariant subspaces is also generalized. Some applications to Hankel operators on discrete groups are given.

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13

Baker, J. W., and A. T. Lau. "Compact left ideal groups in semigroup compactification of locally compact groups." Mathematical Proceedings of the Cambridge Philosophical Society 113, no. 3 (May 1993): 507–17. http://dx.doi.org/10.1017/s0305004100076167.

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Let G be a locally compact group and let UG denote the spectrum of the C*-algebra LUC(G) of bounded left uniformly continuous complex-valued functions on G, with the Gelfand topology. Then there is a multiplication on UG extending the multiplication on G (when naturally embedded in UG) such that UG is a semigroup and for each x ∈ UG, the map y ↦ yx from UG into UG is continuous, i.e. UG is a compact right topological semigroup. Consequently UG has a unique minimal ideal K which is the union of minimal (closed) left ideals UG. Furthermore K is the union of the set of maximal subgroups of K (see [3], theorem 3·ll).

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14

Medghalchi, Alireza, and Ahmad Mollakhalili. "Compact and Weakly Compact Multipliers of Locally Compact Quantum Groups." Bulletin of the Iranian Mathematical Society 44, no. 1 (February 2018): 101–36. http://dx.doi.org/10.1007/s41980-018-0008-y.

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15

Caspers, Martijn. "Locally compact quantum groups." Banach Center Publications 111 (2017): 153–84. http://dx.doi.org/10.4064/bc111-0-5.

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16

Tovmassian, H. M., H. Tiersch, S. G. Navarro, V. H. Chavushyan, G. H. Tovmassian, and S. Neizvestny. "Shakhbazian compact galaxy groups." Astronomy & Astrophysics 415, no. 3 (February 13, 2004): 803–11. http://dx.doi.org/10.1051/0004-6361:20034627.

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17

Tovmassian, H., H. Tiersch, V. H. Chavushyan, G. H. Tovmassian, S. G. Navarro, S. Neizvestny, and J. P. Torres-Papaqui. "Shakhbazian compact galaxy groups." Astronomy & Astrophysics 439, no. 3 (August 12, 2005): 973–79. http://dx.doi.org/10.1051/0004-6361:20042053.

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18

Hernquist, Lars, Neal Katz, and David H. Weinberg. "Physically detached 'compact groups'." Astrophysical Journal 442 (March 1995): 57. http://dx.doi.org/10.1086/175421.

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19

Hickson, Paul. "COMPACT GROUPS OF GALAXIES." Annual Review of Astronomy and Astrophysics 35, no. 1 (September 1997): 357–88. http://dx.doi.org/10.1146/annurev.astro.35.1.357.

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20

Liber, S. A. "Absolutes of compact groups." Russian Mathematical Surveys 40, no. 2 (April 30, 1985): 217–18. http://dx.doi.org/10.1070/rm1985v040n02abeh003567.

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21

Lim, Arthur, and Chen-Bo Zhu. "Multiresolution on compact groups." Linear Algebra and its Applications 293, no. 1-3 (May 1999): 15–38. http://dx.doi.org/10.1016/s0024-3795(99)00018-x.

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22

de Oliveira, Claudia Mendes, and Philippe Amram. "Compact and Fossil Groups." Proceedings of the International Astronomical Union 2, S235 (August 2006): 160–64. http://dx.doi.org/10.1017/s1743921306005850.

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AbstractWe present a short review on poor groups of galaxies focusing on the evolution of compact groups and formation of fossil groups. Fossil groups are systems with one dominant luminous elliptical galaxy surrounded by faint companions, in an extended X-ray halo. We will briefly discuss the possibility of fossil groups being the end-products of the merging of compact groups.

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23

Pildis, Rachel. "Compact Groups of Galaxies." Publications of the Astronomical Society of the Pacific 107 (December 1995): 1259. http://dx.doi.org/10.1086/133685.

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24

KUSTERMANS, J., and S. VAES. "Locally compact quantum groups." Annales Scientifiques de l’École Normale Supérieure 33, no. 6 (November 2000): 837–934. http://dx.doi.org/10.1016/s0012-9593(00)01055-7.

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25

Kitchens, Bruce, and Klaus Schmidt. "Automorphisms of compact groups." Ergodic Theory and Dynamical Systems 9, no. 4 (December 1989): 691–735. http://dx.doi.org/10.1017/s0143385700005290.

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AbstractWe study finitely generated, abelian groups Γ of continuous automorphisms of a compact, metrizable group X and introduce the descending chain condition for such pairs (X, Γ). If Γ acts expansively on X then (X, Γ) satisfies the descending chain condition, and (X, Γ) satisfies the descending chain condition if and only if it is algebraically and topologically isomorphic to a closed, shift-invariant subgroup of GΓ, where G is a compact Lie group. Furthermore every such subgroup of GΓ is a (higher dimensional) Markov shift whose alphabet is a compact Lie group. By using the descending chain condition we prove, for example, that the set of Γ-periodic points is dense in X whenever Γ acts expansively on X. Furthermore, if X is a compact group and (X, Γ) satisfies the descending chain condition, then every ergodic element of Γ has a dense set of periodic points. Finally we give an algebraic description of pairs (X, Γ) satisfying the descending chain condition under the assumption that X is abelian.

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26

Sanchis, Manuel, and Artur Hideyuki Tomita. "Almost p-compact groups." Topology and its Applications 159, no. 9 (June 2012): 2513–27. http://dx.doi.org/10.1016/j.topol.2011.12.025.

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27

Dikranjan, Dikran N., and V. V. Uspenskij. "Categorically compact topological groups." Journal of Pure and Applied Algebra 126, no. 1-3 (April 1998): 149–68. http://dx.doi.org/10.1016/s0022-4049(96)00139-9.

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28

Hickson, P. "Compact Groups of Galaxies." Symposium - International Astronomical Union 186 (1999): 367–73. http://dx.doi.org/10.1017/s0074180900113130.

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This paper reviews some of the outstanding questions concerning compact groups of galaxies. These relate to the physical nature and dynamical status of the groups, their formation and evolution, and their role in galaxy evolution. The picture that emerges is that compact groups are generally physically dense systems, although often contaminated by optical projections. Their evolution is likely a continuous process of infall, interaction and merging. As new galaxies are added, and previous ones merge, the membership of the group evolves. I suggest that while the size of the group changes little, other physical properties such as total mass, gas mass, velocity dispersion, fraction of early-type galaxies increase with time. This picture is at least qualitatively consistent with observations and provides a natural explanation for the strongest correlations found in compact group samples.

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29

Khukhro, E. I., and P. Shumyatsky. "Almost Engel compact groups." Journal of Algebra 500 (April 2018): 439–56. http://dx.doi.org/10.1016/j.jalgebra.2017.04.021.

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30

Rudin, Walter. "Autohomeomorphisms of compact groups." Topology and its Applications 52, no. 1 (August 1993): 69–70. http://dx.doi.org/10.1016/0166-8641(93)90091-q.

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31

Alas, O. T., and M. Sanchis. "Countably Compact Paratopological Groups." Semigroup Forum 74, no. 3 (May 1, 2007): 423–38. http://dx.doi.org/10.1007/s00233-006-0637-y.

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32

Tiersch, H., H. M. Tovmassian, D. Stoll, A. S. Amirkhanian, S. Neizvestny, H. Böhringer, and H. T. MacGillivray. "Shakhbazian compact galaxy groups." Astronomy & Astrophysics 392, no. 1 (August 22, 2002): 33–52. http://dx.doi.org/10.1051/0004-6361:20020877.

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33

Tovmassian, H. M., H. Tiersch, V. H. Chavushyan, and G. H. Tovmassian. "Shakhbazian compact galaxy groups." Astronomy & Astrophysics 401, no. 2 (March 21, 2003): 463–70. http://dx.doi.org/10.1051/0004-6361:20030129.

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34

Zelenyuk, E. G., and I. V. Protasov. "POTENTIALLY COMPACT ABELIAN GROUPS." Mathematics of the USSR-Sbornik 69, no. 1 (February 28, 1991): 299–305. http://dx.doi.org/10.1070/sm1991v069n01abeh001239.

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35

EDMUNDO, MÁRIO J., and MARGARITA OTERO. "DEFINABLY COMPACT ABELIAN GROUPS." Journal of Mathematical Logic 04, no. 02 (December 2004): 163–80. http://dx.doi.org/10.1142/s0219061304000358.

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Let M be an o-minimal expansion of a real closed field. Let G be a definably compact definably connected abelian n-dimensional group definable in M. We show the following: the o-minimal fundamental group of G is isomorphic to ℤn; for each k>0, the k-torsion subgroup of G is isomorphic to (ℤ/kℤ)n, and the o-minimal cohomology algebra over ℚ of G is isomorphic to the exterior algebra over ℚ with n generators of degree one.

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36

Tovmassian, H. M., J. P. Torres-Papaqui, and H. Tiersch. "Isolated Shakhbazian compact groups." Astrophysics 53, no. 3 (July 2010): 320–28. http://dx.doi.org/10.1007/s10511-010-9123-z.

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37

Kubiś, Wieslaw. "Valdivia compact Abelian groups." Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 102, no. 2 (September 2008): 193–97. http://dx.doi.org/10.1007/bf03191818.

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38

De Commer, Kenny, and Thomas Timmermann. "Partial compact quantum groups." Journal of Algebra 438 (September 2015): 283–324. http://dx.doi.org/10.1016/j.jalgebra.2015.04.039.

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39

Medvedev, Yuri. "On compact engel groups." Israel Journal of Mathematics 135, no. 1 (December 2003): 147–56. http://dx.doi.org/10.1007/bf02776054.

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40

Zelmanov, E. I. "On periodic compact groups." Israel Journal of Mathematics 77, no. 1-2 (February 1992): 83–95. http://dx.doi.org/10.1007/bf02808012.

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41

Stroppel, Markus. "Homogeneous Locally Compact Groups." Journal of Algebra 199, no. 2 (January 1998): 528–43. http://dx.doi.org/10.1006/jabr.1997.7202.

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42

Bowen, Lewis, and Peter Burton. "Locally compact sofic groups." Israel Journal of Mathematics 251, no. 1 (December 2022): 239–70. http://dx.doi.org/10.1007/s11856-022-2431-2.

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43

Shtern, Alexander I. "The structure of homomorphisms of connected locally compact groups into compact groups." Izvestiya: Mathematics 75, no. 6 (December 20, 2011): 1279–304. http://dx.doi.org/10.1070/im2011v075n06abeh002572.

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44

Dikranjan, Dikran N., and Dmitrii B. Shakhmatov. "Compact-like totally dense subgroups of compact groups." Proceedings of the American Mathematical Society 114, no. 4 (April 1, 1992): 1119. http://dx.doi.org/10.1090/s0002-9939-1992-1081694-2.

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45

Kachi, Hideyuki, and Mamoru Mimura. "Homotopy groups of compact exceptional Lie groups." Proceedings of the Japan Academy, Series A, Mathematical Sciences 75, no. 4 (April 1999): 47–49. http://dx.doi.org/10.3792/pjaa.75.47.

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46

Wu, T. S. "Automorphism groups of locally compact reductive groups." Proceedings of the American Mathematical Society 106, no. 2 (February 1, 1989): 537. http://dx.doi.org/10.1090/s0002-9939-1989-0968626-x.

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47

Carderi, A., and F. Le Maître. "Orbit full groups for locally compact groups." Transactions of the American Mathematical Society 370, no. 4 (November 30, 2017): 2321–49. http://dx.doi.org/10.1090/tran/6985.

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48

Chirvasitu, Alexandru, and Issan Patri. "Topological automorphism groups of compact quantum groups." Mathematische Zeitschrift 290, no. 1-2 (January 11, 2018): 577–98. http://dx.doi.org/10.1007/s00209-017-2032-7.

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49

Jones, John, Dmitriy Rumynin, and Adam Thomas. "Compact Lie groups and complex reductive groups." Homology, Homotopy and Applications 26, no. 1 (2024): 177–88. http://dx.doi.org/10.4310/hha.2024.v26.n1.a12.

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50

Bavuma, Yanga, and Francesco G. Russo. "Embeddings of locally compact abelian p-groups in Hawaiian groups." Forum Mathematicum 34, no. 1 (December 1, 2021): 97–114. http://dx.doi.org/10.1515/forum-2021-0085.

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Abstract We show that locally compact abelian p-groups can be embedded in the first Hawaiian group on a compact path connected subspace of the Euclidean space of dimension four. This result gives a new geometric interpretation for the classification of locally compact abelian groups which are rich in commuting closed subgroups. It is then possible to introduce the idea of an algebraic topology for topologically modular locally compact groups via the geometry of the Hawaiian earring. Among other things, we find applications for locally compact groups which are just noncompact.

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