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Journal articles on the topic 'Group actions'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Tsai, Jessica Chia-Chin, Natalie Sebanz, and Günther Knoblich. "The GROOP effect: Groups mimic group actions." Cognition 118, no. 1 (January 2011): 135–40. http://dx.doi.org/10.1016/j.cognition.2010.10.007.

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2

CARBONE, LISA, and ELIYAHU RIPS. "RECONSTRUCTING GROUP ACTIONS." International Journal of Algebra and Computation 23, no. 02 (March 2013): 255–323. http://dx.doi.org/10.1142/s021819671340002x.

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We give a general structure theory for reconstructing non-trivial group actions on sets without any further assumptions on the group, the action, or the set on which the group acts. Using certain "local data" [Formula: see text] from the action we build a group [Formula: see text] of the data and a space [Formula: see text] with an action of [Formula: see text] on [Formula: see text] that arise naturally from the data [Formula: see text]. We use these to obtain an approximation to the original group G, the original space X and the original action G × X → X. The data [Formula: see text] is distinguished by the property that it may be chosen from the action locally. For a large enough set of local data [Formula: see text], our definition of [Formula: see text] in terms of generators and relations allows us to obtain a presentation for the group G. We demonstrate this on several examples. When the local data [Formula: see text] is chosen from a graph of groups, the group [Formula: see text] is the fundamental group of the graph of groups and the space [Formula: see text] is the universal covering tree of groups. For general non-properly discontinuous group actions our local data allows us to imitate a fundamental domain, quotient space and universal covering for the quotient. We exhibit this on a non-properly discontinuous free action on ℝ. For a certain class of non-properly discontinuous group actions on the upper half-plane, we use our local data to build a space on which the group acts discretely and cocompactly. Our combinatorial approach to reconstructing abstract group actions on sets is a generalization of the Bass–Serre theory for reconstructing group actions on trees. Our results also provide a generalization of the notion of developable complexes of groups by Haefliger.

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3

Müller, Gerd. "Deformations of reductive group actions." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 1 (July 1989): 77–88. http://dx.doi.org/10.1017/s0305004100067992.

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Consider actions of a reductive complex Lie group G on an analytic space germ (X, 0). In a previous paper [16] we proved that such an action is determined uniquely (up to conjugation with an automorphism of (X, 0)) by the induced action of G on the tangent space of (X, 0). Here it will be shown that every deformation of such an action, parametrized holomorphically by a reduced analytic space germ, is trivial, i.e. can be obtained from the given action by conjugation with a family of automorphisms of (X, 0) depending holomorphically on the parameter. (For a more precise formulation in terms of actions on analytic ℂ-algebras, see Theorem 2 below. An analogue for actions on formal ℂ-algebras is given there too.)

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4

Yalçin, Ergün. "Group actions and group extensions." Transactions of the American Mathematical Society 352, no. 6 (February 24, 2000): 2689–700. http://dx.doi.org/10.1090/s0002-9947-00-02485-5.

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5

Kolganova, Alla. "Chaotic group actions." Bulletin of the Australian Mathematical Society 56, no. 1 (August 1997): 165–67. http://dx.doi.org/10.1017/s0004972700030847.

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6

Wasserman, Arthur G. "Simplifying group actions." Topology and its Applications 75, no. 1 (January 1997): 13–31. http://dx.doi.org/10.1016/s0166-8641(96)00084-3.

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7

Ben Yaacov, Itaï, and Julien Melleray. "Isometrisable group actions." Proceedings of the American Mathematical Society 144, no. 9 (February 17, 2016): 4081–88. http://dx.doi.org/10.1090/proc/13018.

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8

Shi, Enhui, Lizhen Zhou, and Youcheng Zhou. "Chaotic group actions." Applied Mathematics-A Journal of Chinese Universities 18, no. 1 (March 2003): 59–63. http://dx.doi.org/10.1007/s11766-003-0084-4.

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9

Rosenblatt, Joseph. "Ergodic group actions." Archiv der Mathematik 47, no. 3 (September 1986): 263–69. http://dx.doi.org/10.1007/bf01192003.

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10

Oh, Ju-Mok. "Fuzzified group actions." Soft Computing 23, no. 24 (August 7, 2019): 12981–89. http://dx.doi.org/10.1007/s00500-019-04261-3.

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11

Fedorova, M. "Faithful group actions and Schreier graphs." Carpathian Mathematical Publications 9, no. 2 (January 3, 2018): 202–7. http://dx.doi.org/10.15330/cmp.9.2.202-207.

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Each action of a finitely generated group on a set uniquely defines a labelled directed graph called the Schreier graph of the action. Schreier graphs are used mainly as a tool to establish geometrical and dynamical properties of corresponding group actions. In particilar, they are widely used in order to check amenability of different classed of groups. In the present paper Schreier graphs are utilized to construct new examples of faithful actions of free products of groups. Using Schreier graphs of group actions a sufficient condition for a group action to be faithful is presented. This result is applied to finite automaton actions on spaces of words i.e. actions defined by finite automata over finite alphabets. It is shown how to construct new faithful automaton presentations of groups upon given such a presentation. As an example a new countable series of faithful finite automaton presentations of free products of finite groups is constructed. The obtained results can be regarded as another way to construct new faithful actions of groups as soon as at least one such an action is provided.

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12

Chiswell, I. M. "Minimal group actions on Λ-trees." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 1 (1998): 23–36. http://dx.doi.org/10.1017/s030821050002713x.

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We consider the existence and uniqueness of minimal invariant subtrees for abelian actions of groups on Λ-trees, and whether or not a minimal action is determined up to isomorphism by the hyperbolic length function. The main emphasis is on actions of end type. For a trivial action of end type, there is no minimal invariant subtree. However, if a finitely generated group has an action of end type, the action is nontrivial and there is a unique minimal invariant subtree. There are examples of infinitely generated groups with a nontrivial action of end type for which there is no minimal invariant subtree. These results can be used to study actions of cut type.

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13

MEGRELISHVILI, MICHAEL. "Free Topological Groups over (Semi) Group Actions." Annals of the New York Academy of Sciences 788, no. 1 General Topol (May 1996): 164–69. http://dx.doi.org/10.1111/j.1749-6632.1996.tb36808.x.

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14

Kennison, John F. "Pro-group actions and fundamental pro-groups." Journal of Pure and Applied Algebra 66, no. 2 (October 1990): 185–218. http://dx.doi.org/10.1016/0022-4049(90)90084-u.

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15

Johnson, F. E. A. "Extending group actions by finite groups. I." Topology 31, no. 2 (April 1992): 407–20. http://dx.doi.org/10.1016/0040-9383(92)90030-l.

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16

DEELEY, ROBIN J., and KAREN R. STRUNG. "Group actions on Smale space -algebras." Ergodic Theory and Dynamical Systems 40, no. 9 (April 10, 2019): 2368–98. http://dx.doi.org/10.1017/etds.2019.11.

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Group actions on a Smale space and the actions induced on the $\text{C}^{\ast }$-algebras associated to such a dynamical system are studied. We show that an effective action of a discrete group on a mixing Smale space produces a strongly outer action on the homoclinic algebra. We then show that for irreducible Smale spaces, the property of finite Rokhlin dimension passes from the induced action on the homoclinic algebra to the induced actions on the stable and unstable $\text{C}^{\ast }$-algebras. In each of these cases, we discuss the preservation of properties (such as finite nuclear dimension, ${\mathcal{Z}}$-stability, and classification by Elliott invariants) in the resulting crossed products.

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17

Ramsay, Arlan. "Measurable group actions are essentially Borel actions." Israel Journal of Mathematics 51, no. 4 (December 1985): 339–46. http://dx.doi.org/10.1007/bf02764724.

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18

Suksumran, Teerapong. "Gyrogroup actions: A generalization of group actions." Journal of Algebra 454 (May 2016): 70–91. http://dx.doi.org/10.1016/j.jalgebra.2015.12.033.

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19

Abbott, Carolyn, David Hume, and Denis Osin. "Extending group actions on metric spaces." Journal of Topology and Analysis 12, no. 03 (October 1, 2018): 625–65. http://dx.doi.org/10.1142/s1793525319500584.

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We address the following natural extension problem for group actions: Given a group [Formula: see text], a subgroup [Formula: see text], and an action of [Formula: see text] on a metric space, when is it possible to extend it to an action of the whole group [Formula: see text] on a (possibly different) metric space? When does such an extension preserve interesting properties of the original action of [Formula: see text]? We begin by formalizing this problem and present a construction of an induced action which behaves well when [Formula: see text] is hyperbolically embedded in [Formula: see text]. Moreover, we show that induced actions can be used to characterize hyperbolically embedded subgroups. We also obtain some results for elementary amenable groups.

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20

Sharma, Ram Parkash, Anu, and Nirmal Singh. "PARTIAL GROUP ACTIONS ON SEMIALGEBRAS." Asian-European Journal of Mathematics 05, no. 04 (December 2012): 1250060. http://dx.doi.org/10.1142/s179355711250060x.

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For defining a K-semialgebra A, we use Katsov's tensor product which makes the category K-Smod monoidal. Further, if A is a K-semialgebra then AΔ is a KΔ-algebra and A embeds in AΔ. The subtractive and strong partial actions of a group are defined on A. A subtractive partial action α of a group G on A can be extended to a partial action of G on AΔ which helps in globalization of α. A strong partial action on A has a unique subtractive globalization. We also discuss the associativity of the skew group semiring A ×α G.

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21

Gonçalves, Daniel. "Simplicity of Partial Skew Group Rings of Abelian Groups." Canadian Mathematical Bulletin 57, no. 3 (September 1, 2014): 511–19. http://dx.doi.org/10.4153/cmb-2014-011-1.

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AbstractLet A be a ring with local units, E a set of local units for A, G an abelian group, and α a partial action of G by ideals of A that contain local units. We show that A*αG is simple if and only if A is G-simple and the center of the corner eδ0(A*αGe)eδ0 is a field for all e ∊ E. We apply the result to characterize simplicity of partial skew group rings in two cases, namely for partial skew group rings arising from partial actions by clopen subsets of a compact set and partial actions on the set level.

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22

Iyer, Ganesh, and Hema Yoganarasimhan. "Strategic Polarization in Group Interactions." Journal of Marketing Research 58, no. 4 (June 22, 2021): 782–800. http://dx.doi.org/10.1177/00222437211016389.

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The authors study the phenomenon of strategic group polarization, in which members take more extreme actions than their preferences. The analysis is relevant for a broad range of formal and informal group settings, including social media, online platforms, sales teams, corporate and academic committees, and political action committees. In the model, agents with private preferences choose a public action (voice opinions), and the mean of their actions represents the group’s realized outcome. The agents face a trade-off between influencing the group decision and truth-telling. In a simultaneous-move game, agents strategically shade their actions toward the extreme. The strategic group influence motive can create substantial polarization in actions and group decisions even when the preferences are relatively moderate. Compared with a simultaneous game, a randomized-sequential-actions game lowers polarization when agents’ preferences are relatively similar. Sequential actions can even lead to moderation if the later agents have moderate preferences. Endogenizing the order of moves (through a first-price sealed-bid auction) always increases polarization, but it is also welfare enhancing. These findings can help group leaders, firms, and platforms design mechanisms that moderate polarization, such as the choice of speaking order, the group size, and the knowledge members have of others’ preferences and actions.

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23

Kanai, Masahiko. "Rigidity of group actions." Séminaire de théorie spectrale et géométrie 15 (1997): 203–5. http://dx.doi.org/10.5802/tsg.192.

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24

Huru, Hilja L., and Valentin V. Lychagin. "Quantizations of Group Actions." Journal of Generalized Lie Theory and Applications 6 (2012): 1–15. http://dx.doi.org/10.4303/jglta/g120403.

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25

Greenberg, Peter. "Pseudogroups from Group Actions." American Journal of Mathematics 109, no. 5 (October 1987): 893. http://dx.doi.org/10.2307/2374493.

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26

Dydak, Jerzy. "Overlays and group actions." Topology and its Applications 207 (July 2016): 22–32. http://dx.doi.org/10.1016/j.topol.2016.03.031.

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27

Blanc, David, and Debasis Sen. "Realizing homotopy group actions." Bulletin of the Belgian Mathematical Society - Simon Stevin 21, no. 4 (October 2014): 685–710. http://dx.doi.org/10.36045/bbms/1414091009.

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28

Isaacs, I. M. "Group actions and orbits." Archiv der Mathematik 98, no. 5 (March 8, 2012): 399–401. http://dx.doi.org/10.1007/s00013-012-0364-4.

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29

McCullough, Darryl, Andy Miller, and Bruno Zimmermann. "Group Actions on Handlebodies." Proceedings of the London Mathematical Society s3-59, no. 2 (September 1989): 373–416. http://dx.doi.org/10.1112/plms/s3-59.2.373.

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30

Fisher, David. "Deformations of group actions." Transactions of the American Mathematical Society 360, no. 01 (January 1, 2008): 491–506. http://dx.doi.org/10.1090/s0002-9947-07-04372-3.

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31

MELNIKOV, ALEXANDER, and ANTONIO MONTALBÁN. "COMPUTABLE POLISH GROUP ACTIONS." Journal of Symbolic Logic 83, no. 2 (June 2018): 443–60. http://dx.doi.org/10.1017/jsl.2017.68.

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AbstractUsing methods from computable analysis, we establish a new connection between two seemingly distant areas of logic: computable structure theory and invariant descriptive set theory. We extend several fundamental results of computable structure theory to the more general setting of topological group actions. As we will see, the usual action of ${S_\infty }$ on the space of structures in a given language is effective in a certain algorithmic sense that we need, and ${S_\infty }$ itself carries a natural computability structure (to be defined). Among other results, we give a sufficient condition for an orbit under effective ${\cal G}$-action of a computable Polish ${\cal G}$ to split into infinitely many disjoint effective orbits. Our results are not only more general than the respective results in computable structure theory, but they also tend to have proofs different from (and sometimes simpler than) the previously known proofs of the respective prototype results.

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32

Re, Riccardo. "Supersingularity from group actions." Mathematische Nachrichten 281, no. 4 (April 2008): 575–81. http://dx.doi.org/10.1002/mana.200510626.

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33

Puppe, V. "Group Actions and Codes." Canadian Journal of Mathematics 53, no. 1 (February 1, 2001): 212–24. http://dx.doi.org/10.4153/cjm-2001-009-0.

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AbstractA 2-action with “maximal number of isolated fixed points” (i.e., with only isolated fixed points such that dimk(⊕iHi (M; k)) = |M2|, k = ) on a 3-dimensional, closed manifold determines a binary self-dual code of length = . In turn this code determines the cohomology algebra H*(M; k) and the equivariant cohomology . Hence, from results on binary self-dual codes one gets information about the cohomology type of 3-manifolds which admit involutions with maximal number of isolated fixed points. In particular, “most” cohomology types of closed 3-manifolds do not admit such involutions. Generalizations of the above result are possible in several directions, e.g., one gets that “most” cohomology types (over ) of closed 3-manifolds do not admit a non-trivial involution.

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34

Fauntleroy, Amassa. "Unipotent group actions: corrections." Journal of Pure and Applied Algebra 50, no. 2 (February 1988): 209–10. http://dx.doi.org/10.1016/0022-4049(88)90116-8.

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35

Nowak, Piotr W. "Isoperimetry of group actions." Advances in Mathematics 219, no. 1 (September 2008): 1–26. http://dx.doi.org/10.1016/j.aim.2008.04.012.

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36

Radcliffe, A. J., and A. D. Scott. "Reconstructing under Group Actions." Graphs and Combinatorics 22, no. 3 (November 2006): 399–419. http://dx.doi.org/10.1007/s00373-006-0675-y.

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37

Babson, Eric, and Dmitry N. Kozlov. "Group actions on posets." Journal of Algebra 285, no. 2 (March 2005): 439–50. http://dx.doi.org/10.1016/j.jalgebra.2001.07.002.

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38

Delucchi, Emanuele, and Sonja Riedel. "Group actions on semimatroids." Advances in Applied Mathematics 95 (April 2018): 199–270. http://dx.doi.org/10.1016/j.aam.2017.11.001.

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39

Derksen, Harm, and Frank Kutzschebauch. "Nonlinearizable holomorphic group actions." Mathematische Annalen 311, no. 1 (May 1, 1998): 41–53. http://dx.doi.org/10.1007/s002080050175.

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40

Hoshi, Akinari, and Ming-chang Kang. "Twisted symmetric group actions." Pacific Journal of Mathematics 248, no. 2 (December 1, 2010): 285–304. http://dx.doi.org/10.2140/pjm.2010.248.285.

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41

Zimmer, Robert J. "Groups generating transversals to semisimple lie group actions." Israel Journal of Mathematics 73, no. 2 (June 1991): 151–59. http://dx.doi.org/10.1007/bf02772946.

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42

Br�stle, T., G. R�hrle, and L. Hille. "Finiteness for parabolic group actions in classical groups." Archiv der Mathematik 76, no. 2 (February 1, 2001): 81–87. http://dx.doi.org/10.1007/s000130050545.

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43

Humphries, Stephen P. "Finite Hurwitz braid group actions for Artin groups." Israel Journal of Mathematics 143, no. 1 (December 2004): 189–222. http://dx.doi.org/10.1007/bf02803499.

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44

Wilking, Burkhard. "Rigidity of group actions on solvable Lie groups." Mathematische Annalen 317, no. 2 (June 1, 2000): 195–237. http://dx.doi.org/10.1007/s002089900091.

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45

Tamminga, Allard, and Hein Duijf. "COLLECTIVE OBLIGATIONS, GROUP PLANS AND INDIVIDUAL ACTIONS." Economics and Philosophy 33, no. 2 (November 23, 2016): 187–214. http://dx.doi.org/10.1017/s0266267116000213.

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Abstract:If group members aim to fulfil a collective obligation, they must act in such a way that the composition of their individual actions amounts to a group action that fulfils the collective obligation. We study a strong sense of joint action in which the members of a group design and then publicly adopt a group plan that coordinates the individual actions of the group members. We characterize the conditions under which a group plan successfully coordinates the group members’ individual actions, and study how the public adoption of a plan changes the context in which individual agents make a decision about what to do.

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46

Kamber, Franz W., and Peter W. Michor. "Completing Lie algebra actions to Lie group actions." Electronic Research Announcements of the American Mathematical Society 10, no. 1 (February 18, 2004): 1–10. http://dx.doi.org/10.1090/s1079-6762-04-00124-6.

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47

KELLENDONK, J., and MARK V. LAWSON. "PARTIAL ACTIONS OF GROUPS." International Journal of Algebra and Computation 14, no. 01 (February 2004): 87–114. http://dx.doi.org/10.1142/s0218196704001657.

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A partial action of a group G on a set X is a weakening of the usual notion of a group action: the function G×X→X that defines a group action is replaced by a partial function; in addition, the existence of g·(h·x) implies the existence of (gh)·x, but not necessarily conversely. Such partial actions are extremely widespread in mathematics, and the main aim of this paper is to prove two basic results concerning them. First, we obtain an explicit description of Exel's universal inverse semigroup [Formula: see text], which has the property that partial actions of the group G give rise to actions of the inverse semigroup [Formula: see text]. We apply this result to the theory of graph immersions. Second, we prove that each partial group action is the restriction of a universal global group action. We describe some applications of this result to group theory and the theory of E-unitary inverse semigroups.

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48

DANILENKO, ALEXANDRE I. "Mixing actions of the Heisenberg group." Ergodic Theory and Dynamical Systems 34, no. 4 (January 21, 2013): 1142–67. http://dx.doi.org/10.1017/etds.2012.169.

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AbstractMixing (of all orders) rank-one actions $T$ of the Heisenberg group ${H}_{3} ( \mathbb{R} )$ are constructed. The restriction of $T$ to the center of ${H}_{3} ( \mathbb{R} )$ is simple and commutes only with $T$. Mixing Poisson and mixing Gaussian actions of ${H}_{3} ( \mathbb{R} )$ are also constructed. A rigid weakly mixing rank-one action $T$ is constructed such that the restriction of $T$ to the center of ${H}_{3} ( \mathbb{R} )$ is not isomorphic to its inverse.

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49

Godinho, Leonor, and M. E. Sousa-Dias. "The Fundamental Group ofS1-manifolds." Canadian Journal of Mathematics 62, no. 5 (October 1, 2010): 1082–98. http://dx.doi.org/10.4153/cjm-2010-053-3.

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AbstractWe address the problem of computing the fundamental group of a symplecticS1-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a HamiltonianS1-action. Several examples are presented to illustrate our main results.

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50

Isaacs, I. M. "Dual modules and group actions on extra-special groups." Rocky Mountain Journal of Mathematics 18, no. 3 (September 1988): 505–18. http://dx.doi.org/10.1216/rmj-1988-18-3-505.

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