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Artigos de revistas sobre o tema "Reductive group schemes"

Autor: Grafiati

Publicado: 5 de outubro de 2024

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1

Pan, Yang. "Saturation rank for finite group schemes: Finite groups and infinitesimal group schemes." Forum Mathematicum 30, no. 2 (2018): 479–95. http://dx.doi.org/10.1515/forum-2017-0007.

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AbstractWe investigate the saturation rank of a finite group scheme defined over an algebraically closed field{\Bbbk}of positive characteristicp. We begin by exploring the saturation rank for finite groups and infinitesimal group schemes. Special attention is given to reductive Lie algebras and the second Frobenius kernel of the algebraic group{\operatorname{SL}_{n}}.

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2

González-Avilés, Cristian D. "Abelian class groups of reductive group schemes." Israel Journal of Mathematics 196, no. 1 (2013): 175–214. http://dx.doi.org/10.1007/s11856-012-0147-4.

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3

MCNINCH, GEORGE. "REDUCTIVE SUBGROUP SCHEMES OF A PARAHORIC GROUP SCHEME." Transformation Groups 25, no. 1 (2018): 217–49. http://dx.doi.org/10.1007/s00031-018-9508-3.

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4

Gyoja, Akihiko. "Representations of reductive group schemes." Tsukuba Journal of Mathematics 15, no. 2 (1991): 335–46. http://dx.doi.org/10.21099/tkbjm/1496161661.

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5

Prasad, Gopal, and Jiu-Kang Yu. "On quasi-reductive group schemes." Journal of Algebraic Geometry 15, no. 3 (2006): 507–49. http://dx.doi.org/10.1090/s1056-3911-06-00422-x.

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6

Waterhouse, William C. "Geometrically reductive affine group schemes." Archiv der Mathematik 62, no. 4 (1994): 306–7. http://dx.doi.org/10.1007/bf01201781.

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7

Vasiu, Adrian. "Extension theorems for reductive group schemes." Algebra & Number Theory 10, no. 1 (2016): 89–115. http://dx.doi.org/10.2140/ant.2016.10.89.

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8

Zhao, Yifei. "Tannakian reconstruction of reductive group schemes." Pacific Journal of Mathematics 321, no. 2 (2022): 467–78. http://dx.doi.org/10.2140/pjm.2022.321.467.

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9

Stasinski, Alexander. "Reductive group schemes, the Greenberg functor, and associated algebraic groups." Journal of Pure and Applied Algebra 216, no. 5 (2012): 1092–101. http://dx.doi.org/10.1016/j.jpaa.2011.10.027.

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10

CHANG, HAO, and ROLF FARNSTEINER. "Finite group schemes of p-rank ≤ 1." Mathematical Proceedings of the Cambridge Philosophical Society 166, no. 2 (2017): 297–323. http://dx.doi.org/10.1017/s0305004117000834.

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AbstractLet be a finite group scheme over an algebraically closed field k of characteristic char(k) = p ≥ 3. In generalisation of the familiar notion from the modular representation theory of finite groups, we define the p-rank rkp() of and determine the structure of those group schemes of p-rank 1, whose linearly reductive radical is trivial. The most difficult case concerns infinitesimal groups of height 1, which correspond to restricted Lie algebras. Our results show that group schemes of p-rank ≤ 1 are closely related to those being of finite or domestic representation type.

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11

Alper, Jared. "Adequate moduli spaces and geometrically reductive group schemes." Algebraic Geometry 1, no. 4 (2014): 489–531. http://dx.doi.org/10.14231/ag-2014-022.

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12

Alexeev, Valery, and Michel Brion. "Moduli of affine schemes with reductive group action." Journal of Algebraic Geometry 14, no. 1 (2005): 83–117. http://dx.doi.org/10.1090/s1056-3911-04-00377-7.

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13

Behrend, Kai A. "Semi-stability of reductive group schemes over curves." Mathematische Annalen 301, no. 1 (1995): 281–305. http://dx.doi.org/10.1007/bf01446630.

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14

Anschütz, Johannes. "Reductive group schemes over the Fargues–Fontaine curve." Mathematische Annalen 374, no. 3-4 (2018): 1219–60. http://dx.doi.org/10.1007/s00208-018-1785-6.

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15

Gille, Philippe, and Arturo Pianzola. "Torsors, reductive group schemes and extended affine Lie algebras." Memoirs of the American Mathematical Society 226, no. 1063 (2013): 1. http://dx.doi.org/10.1090/s0065-9266-2013-00679-x.

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16

Chernousov, V., P. Gille, and A. Pianzola. "Conjugacy theorems for loop reductive group schemes and Lie algebras." Bulletin of Mathematical Sciences 4, no. 2 (2014): 281–324. http://dx.doi.org/10.1007/s13373-014-0052-8.

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17

Lehn, Christian, and Ronan Terpereau. "Invariant deformation theory of affine schemes with reductive group action." Journal of Pure and Applied Algebra 219, no. 9 (2015): 4168–202. http://dx.doi.org/10.1016/j.jpaa.2015.02.013.

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18

Satriano, Matthew. "The Chevalley–Shephard–Todd theorem for finite linearly reductive group schemes." Algebra & Number Theory 6, no. 1 (2012): 1–26. http://dx.doi.org/10.2140/ant.2012.6.1.

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19

Panin, I., A. Stavrova, and N. Vavilov. "On Grothendieck–Serre’s conjecture concerning principal -bundles over reductive group schemes: I." Compositio Mathematica 151, no. 3 (2014): 535–67. http://dx.doi.org/10.1112/s0010437x14007635.

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AbstractLet$k$be an infinite field. Let$R$be the semi-local ring of a finite family of closed points on a$k$-smooth affine irreducible variety, let$K$be the fraction field of$R$, and let$G$be a reductive simple simply connected$R$-group scheme isotropic over$R$. Our Theorem 1.1 states that for any Noetherian$k$-algebra$A$the kernel of the map$$\begin{eqnarray}H_{\acute{\text{e}}\text{t}}^{1}(R\otimes _{k}A,G)\rightarrow H_{\acute{\text{e}}\text{t}}^{1}(K\otimes _{k}A,G)\end{eqnarray}$$induced by the inclusion of$R$into$K$is trivial. Theorem 1.2 for$A=k$and some other results of the present pap

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20

Panin, I. A. "On Grothendieck-Serre's conjecture concerning principalG-bundles over reductive group schemes: II." Izvestiya: Mathematics 80, no. 4 (2016): 759–90. http://dx.doi.org/10.1070/im8452.

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21

Sopkina, Ekaterina. "Classification of all connected subgroup schemes of a reductive group containing a split maximal torus." Journal of K-Theory 3, no. 1 (2008): 103–22. http://dx.doi.org/10.1017/is008007004jkt043.

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AbstractThe main result of the paper is a classification of all connected subgroup schemes of a reductive group containing a split maximal torus, over an arbitrary field. The classification is expressed in terms of functions on the root system.

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22

Панин, Иван Александрович, and Ivan Alexandrovich Panin. "On Grothendieck - Serre's conjecture concerning principal $G$-bundles over reductive group schemes: II." Известия Российской академии наук. Серия математическая 80, no. 4 (2016): 131–62. http://dx.doi.org/10.4213/im8452.

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23

Thăńg, Nguyêñ Quôć. "Corestriction principle for non-abelian cohomology of reductive group schemes over arithmetical rings." Proceedings of the Japan Academy, Series A, Mathematical Sciences 82, no. 9 (2006): 147–51. http://dx.doi.org/10.3792/pjaa.82.147.

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24

Zhao, Yifei. "Spectral decomposition of genuine cusp forms over global function fields." Compositio Mathematica 160, no. 6 (2024): 1194–260. http://dx.doi.org/10.1112/s0010437x24007127.

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We prove the geometric Satake equivalence for étale metaplectic covers of reductive group schemes and extend the Langlands parametrization of V. Lafforgue to genuine cusp forms defined on their associated covering groups.

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25

Panin, Ivan. "Nice triples and the Grothendieck–Serre conjecture concerning principal G-bundles over reductive group schemes." Duke Mathematical Journal 168, no. 2 (2019): 351–75. http://dx.doi.org/10.1215/00127094-2018-0042.

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26

Thǎńg, Nguyêñ Quôć. "A Norm Principle for Class Groups of Reductive Group Schemes over Dedekind Rings of Integers of Local and Global Fields." Vietnam Journal of Mathematics 43, no. 2 (2015): 257–81. http://dx.doi.org/10.1007/s10013-015-0122-6.

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27

Bültel, O., and G. Pappas. "-DISPLAYS AND RAPOPORT–ZINK SPACES." Journal of the Institute of Mathematics of Jussieu 19, no. 4 (2018): 1211–57. http://dx.doi.org/10.1017/s1474748018000373.

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Let $(G,\unicode[STIX]{x1D707})$ be a pair of a reductive group $G$ over the $p$-adic integers and a minuscule cocharacter $\unicode[STIX]{x1D707}$ of $G$ defined over an unramified extension. We introduce and study ‘$(G,\unicode[STIX]{x1D707})$-displays’ which generalize Zink’s Witt vector displays. We use these to define certain Rapoport–Zink formal schemes purely group theoretically, i.e. without $p$-divisible groups.

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28

Conrad, Brian. "Finiteness theorems for algebraic groups over function fields." Compositio Mathematica 148, no. 2 (2011): 555–639. http://dx.doi.org/10.1112/s0010437x11005665.

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AbstractWe prove the finiteness of class numbers and Tate–Shafarevich sets for all affine group schemes of finite type over global function fields, as well as the finiteness of Tamagawa numbers and Godement’s compactness criterion (and a local analogue) for all such groups that are smooth and connected. This builds on the known cases of solvable and semi-simple groups via systematic use of the recently developed structure theory and classification of pseudo-reductive groups.

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29

Wenzel, Christian. "Classification of all parabolic subgroup-schemes of a reductive linear algebraic group over an algebraically closed field." Transactions of the American Mathematical Society 337, no. 1 (1993): 211–18. http://dx.doi.org/10.1090/s0002-9947-1993-1096262-1.

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30

Knop, Friedrich, and Gerhard Röhrle. "Spherical subgroups in simple algebraic groups." Compositio Mathematica 151, no. 7 (2015): 1288–308. http://dx.doi.org/10.1112/s0010437x1400791x.

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Let $G$ be a simple algebraic group. A closed subgroup $H$ of $G$ is said to be spherical if it has a dense orbit on the flag variety $G/B$ of $G$. Reductive spherical subgroups of simple Lie groups were classified by Krämer in 1979. In 1997, Brundan showed that each example from Krämer’s list also gives rise to a spherical subgroup in the corresponding simple algebraic group in any positive characteristic. Nevertheless, up to now there has been no classification of all such instances in positive characteristic. The goal of this paper is to complete this classification. It turns out that there

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31

BRION, M., and R. JOSHUA. "NOTIONS OF PURITY AND THE COHOMOLOGY OF QUIVER MODULI." International Journal of Mathematics 23, no. 09 (2012): 1250097. http://dx.doi.org/10.1142/s0129167x12500978.

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We explore several variations of the notion of purity for the action of Frobenius on schemes defined over finite fields. In particular, we study how these notions are preserved under certain natural operations like quotients for principal bundles and also geometric quotients for reductive group actions. We then apply these results to study the cohomology of quiver moduli. We prove that a natural stratification of the space of representations of a quiver with a fixed dimension vector is equivariantly perfect and from it deduce that each of the l-adic cohomology groups of the quiver moduli space

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32

Groechenig, Michael. "Adelic descent theory." Compositio Mathematica 153, no. 8 (2017): 1706–46. http://dx.doi.org/10.1112/s0010437x17007217.

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A result of André Weil allows one to describe rank $n$ vector bundles on a smooth complete algebraic curve up to isomorphism via a double quotient of the set $\text{GL}_{n}(\mathbb{A})$ of regular matrices over the ring of adèles (over algebraically closed fields, this result is also known to extend to $G$-torsors for a reductive algebraic group $G$). In the present paper we develop analogous adelic descriptions for vector and principal bundles on arbitrary Noetherian schemes, by proving an adelic descent theorem for perfect complexes. We show that for Beilinson’s co-simplicial ring of adèles

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33

Bernardini, Riccardo, Roberto Cesco Fabbro, and Roberto Rinaldo. "Group-Based Reduction Schemes for Streaming Applications." ISRN Communications and Networking 2011 (September 8, 2011): 1–10. http://dx.doi.org/10.5402/2011/898254.

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Some peer-to-peer streaming systems make use of linear codes to reduce the rate of the data uploaded by peers with limited upload capabilities. Such “data reduction” techniques are based on a vector-space approach and produce the data to be uploaded by means of linear combinations of the content data in a suitable finite field. In this paper, we propose a more general approach based on group theory. The new approach, while including the vector space approach as a special case, allows to design schemes that cannot be modeled as linear codes. We analyze the properties of the schemes based on the

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34

Vasiu, Adrian. "Normal, unipotent subgroup schemes of reductive groups." Comptes Rendus Mathematique 341, no. 2 (2005): 79–84. http://dx.doi.org/10.1016/j.crma.2005.05.014.

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35

Howard, Benjamin, and Georgios Pappas. "Rapoport–Zink spaces for spinor groups." Compositio Mathematica 153, no. 5 (2017): 1050–118. http://dx.doi.org/10.1112/s0010437x17007011.

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After the work of Kisin, there is a good theory of canonical integral models of Shimura varieties of Hodge type at primes of good reduction. The first part of this paper develops a theory of Hodge type Rapoport–Zink formal schemes, which uniformize certain formal completions of such integral models. In the second part, the general theory is applied to the special case of Shimura varieties associated with groups of spinor similitudes, and the reduced scheme underlying the Rapoport–Zink space is determined explicitly.

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36

SUFIANI, R., S. NAMI, M. GOLMOHAMMADI, and M. A. JAFARIZADEH. "CONTINUOUS TIME QUANTUM WALKS AND QUOTIENT GRAPHS." International Journal of Quantum Information 09, no. 03 (2011): 1005–17. http://dx.doi.org/10.1142/s0219749911007435.

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Continuous-time quantum walks (CTQW) over finite group schemes is investigated, where it is shown that some properties of a CTQW over a group scheme defined on a finite group G induces a CTQW over group scheme defined on G/H, where H is a normal subgroup of G with prime index. This reduction can be helpful in analyzing CTQW on underlying graphs of group schemes. Even though this claim is proved for normal subgroups with prime index (using the Clifford's theorem from representation theory), it is checked in some examples that for other normal subgroups or even non-normal subgroups, the result i

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37

Khekan, Ali, and Bernd Kordaß. "Comparing Zirconium Crown Marginal Adaptation in Preparations with Two Different Occlusal Reductions." Dentistry Journal 12, no. 3 (2024): 77. http://dx.doi.org/10.3390/dj12030077.

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This study aimed to assess and contrast the effects on the vertical marginal fit of full contour CAD/CAM-generated monolithic zirconia crowns at pre- and post-cementation levels with various occlusal reduction schemes (planar and flat) and cements. Forty sound human maxillary first premolars were sampled for this study. The samples were divided into two main groups with twenty samples in each group according to the occlusal reduction scheme as follows: Group A included a chamfer finishing line design with a planar occlusal reduction scheme and Group B included a chamfer finishing line design w

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38

Chen, Xi, and Kok Kwang Phoon. "Applications of Symmetric and Nonsymmetric MSSOR Preconditioners to Large-Scale Biot's Consolidation Problems with Nonassociated Plasticity." Journal of Applied Mathematics 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/352081.

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Two solution schemes are proposed and compared for large 3D soil consolidation problems with nonassociated plasticity. One solution scheme results in the nonsymmetric linear equations due to the Newton iteration, while the other leads to the symmetric linear systems due to the symmetrized stiffness strategies. To solve the resulting linear systems, the QMR and SQMR solver are employed in conjunction with nonsymmetric and symmetric MSSOR preconditioner, respectively. A simple footing example and a pile-group example are used to assess the performance of the two solution schemes. Numerical resul

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39

Grossi, Sonia Aurora Alves, Simão Augusto Lottenberg, Ana Maria Lottenberg, Thaís Della Manna, and Hilton Kuperman. "Home blood glucose monitoring in type 1 diabetes mellitus." Revista Latino-Americana de Enfermagem 17, no. 2 (2009): 194–200. http://dx.doi.org/10.1590/s0104-11692009000200009.

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OBJECTIVE: To determine which of two simplified blood glucose monitoring schemes promotes better metabolic control in type1 diabetic patients during 12 months of participation in educational groups. METHODS: A crossover clinical trial involving 21 patients divided into two groups was conducted. They were submitted to a two monitoring schemes:2 alternate daily preprandial measurements and 2 alternate daily pre-and postprandial measurements. The effectiveness of the schemes was evaluated based on HbA1c. Variations in mean HbA1c were analyzed by Friedman test. RESULTS: The groups were homogenous

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40

Lahire, Bernard. "De la teoría del habitus a una sociología psicológica." CPU-e, Revista de Investigación Educativa, no. 14 (October 30, 2012): 75–105. http://dx.doi.org/10.25009/cpue.v0i14.30.

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En este texto, Bernard Lahire desarrolla las bases de un programa de sociología psicológica, y en el camino, deja ver por qué no sólo es deseable sino necesaria la interacción de disciplinas como la sociología, la antropología y la psicología. Por ejemplo, expone que el concepto bourdiano de habitus tiene su origen en el concepto piagetiano de esquema de acción, con lo que se muestra que, reconociéndolo o no, existe de hecho una fuerte interacción entre disciplinas. Además, este texto permite refrescar las reflexiones acerca de la cultura, las identidades, la socialización y las mentes de los

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41

Thanh, Nga, Khanh Kim, Son Hong, and Trung Lam. "Entropy Correlation and Its Impacts on Data Aggregation in a Wireless Sensor Network." Sensors 18, no. 9 (2018): 3118. http://dx.doi.org/10.3390/s18093118.

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A correlation characteristic has significant potential advantages for the development of efficient communication protocols in wireless sensor networks (WSNs). To exploit the correlation in WSNs, the correlation model is required. However, most of the present correlation models are linear and distance-dependent. This paper proposes a general distance-independent entropy correlation model based on the relation between joint entropy and the number of members in a group. This relation is estimated using entropy of individual members and entropy correlation coefficients of member pairs. The propose

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Guo, Zhuo Tuan, Yong Guo, Di Wu, Jun Peng, Yong Bing Wang, and Sheng Li An. "Production Process Optimization of Mongolian Iron Ore Pellets for Baogang Group." Applied Mechanics and Materials 751 (April 2015): 35–39. http://dx.doi.org/10.4028/www.scientific.net/amm.751.35.

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Baogang Group imported large quantities of Mongolian iron ore to solve the shortage of ironmaking raw materials. But the basic parameters of Mongolian iron ore in pellets production are deficient. In this paper, orthogonal experimental method was used in the optimization of roasting production process of Mongolian iron ore pellets. The results show that when the content of Mongolian iron ore is 55%, the factors affecting the expansion rate of pellets in order of decrease is bentonite proportion, roasting temperature, roasting time and preheating temperature. For pellets containing 55% Mongolia

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Xu, Guishuang, Xinchun Yin, and Xincheng Li. "ER-CGKA: Efficient and robust continuous group key agreement scheme with post-compromise forward security for IoV." PLOS ONE 19, no. 8 (2024): e0307867. http://dx.doi.org/10.1371/journal.pone.0307867.

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The Internet of Vehicles (IoV) counts for much in advancing intelligent transportation by connecting people, vehicles, infrastructures, and cloud servers (CS). However, the open-access wireless channels within the IoV are susceptible to malicious attacks. Therefore, an authentication key agreement protocol becomes essential to ensure secure vehicular communications and protect vehicle privacy. Nevertheless, although the vehicles in the group are compromised, they can still update the group key and obtain the communication content in the existing group key agreement protocols. Therefore, it is

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Ha, Sook S., Inyoung Kim, Yue Wang, and Jianhua Xuan. "Applications of Different Weighting Schemes to Improve Pathway-Based Analysis." Comparative and Functional Genomics 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/463645.

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Conventionally, pathway-based analysis assumes that genes in a pathway equally contribute to a biological function, thus assigning uniform weight to genes. However, this assumption has been proved incorrect, and applying uniform weight in the pathway analysis may not be an appropriate approach for the tasks like molecular classification of diseases, as genes in a functional group may have different predicting power. Hence, we propose to use different weights to genes in pathway-based analysis and devise four weighting schemes. We applied them in two existing pathway analysis methods using both

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45

Guan, Hong, Hao Liu, and Raafat George Saadé. "Analysis of Carbon Emission Reduction in International Civil Aviation through the Lens of Shared Triple Bottom Line Value Creation." Sustainability 14, no. 14 (2022): 8513. http://dx.doi.org/10.3390/su14148513.

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Overall, climate concerns have been on the global agenda for many years now. However, the aviation sector’s impact on climate change has been receiving increased attention recently. This is primarily due to the adoption of the 2016 carbon offsetting and reduction scheme for international civil aviation (CORSIA) which was introduced by the international civil aviation organization (ICAO). The aims of our study are to analyze ICAO’s carbon offsetting reduction scheme through the lens of the triple bottom line (TBL) value creation dimensions and to explore implementation issues relevant to its su

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Kaseniit, Kristjan Eerik, Mark R. Theilmann, Alexander Robertson, Eric A. Evans, and Imran S. Haque. "Group Testing Approach for Trinucleotide Repeat Expansion Disorder Screening." Clinical Chemistry 62, no. 10 (2016): 1401–8. http://dx.doi.org/10.1373/clinchem.2016.259796.

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Abstract BACKGROUND Fragile X syndrome (FXS, OMIM #300624) is an X-linked condition caused by trinucleotide repeat expansions in the 5′ UTR (untranslated region) of the fragile X mental retardation 1 (FMR1) gene. FXS testing is commonly performed in expanded carrier screening and has been proposed for inclusion in newborn screening. However, because pathogenic alleles are long and have low complexity (&gt;200 CGG repeats), FXS is currently tested by a single-plex electrophoresis-resolved PCR assay rather than multiplexed approaches like next-generation sequencing or mass spectrometry. In t

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Dahm, Rolf. "Spin-Flavour Symmetry and Contractions Towards Classical Space-Time Symmetry." International Journal of Modern Physics A 12, no. 01 (1997): 147–52. http://dx.doi.org/10.1142/s0217751x97000190.

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A classification scheme of hadrons is proposed on the basis of the division algebra H of quaternions and an appropriate geometry. This scheme suggests strongly to understand flavour symmetry in another manner than from standard symmetry schemes. In our approach, we do not start from "exact" symmetry groups like SU(2) × SU(2) chiral symmetry and impose various symmetry breaking mechanisms which collide with theorems wellknown from quantum field theory. On the contrary, the approximate symmetry properties of the hadron spectrum at low energies, usually classified by "appropriately" broken compac

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48

Chatterjee, Sanjit, M. Prem Laxman Das, and R. Kabaleeshwaran. "Converting pairing-based cryptosystems from composite to prime order setting – A comparative analysis." Journal of Mathematical Cryptology 12, no. 3 (2018): 159–90. http://dx.doi.org/10.1515/jmc-2017-0042.

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Abstract Composite order pairing setting has been used to achieve cryptographic functionalities beyond what is attainable in prime order groups. However, such pairings are known to be significantly slower than their prime order counterparts. Thus emerged a new line of research – developing frameworks to convert cryptosystems from composite to prime order pairing setting. In this work, we analyse the intricacies of efficient prime order instantiation of cryptosystems that can be converted using existing frameworks. To compare the relative efficacy of these frameworks we mainly focus on some rep

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Tu, Yung-Ping, Zi-Teng Zhan та Yung-Fa Huang. "A Novel Alternating μ-Law Companding Algorithm for PAPR Reduction in OFDM Systems". Electronics 13, № 4 (2024): 694. http://dx.doi.org/10.3390/electronics13040694.

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Orthogonal frequency division multiplexing (OFDM) inherits multi-carrier systems’ inevitable high peak-to-average power ratio (PAPR) problem. In this paper, a novel alternating companding technique is proposed to combat the harassment of high PAPR. The sequential μ-law companding (SULC) and a tone with a lower PAPR result in only partial tones needing companding. The SULC scheme’s PAPR and bit error rate (BER) performance has been balanced and improved. However, the computational complexity is still too high to be implemented. Therefore, this study sorted the transmission signals according to

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Aparna, R., and B. B. Amberker. "Key Management Schemes for Multilayer and Multiple Simultaneous Secure Group Communication." ISRN Communications and Networking 2012 (August 1, 2012): 1–11. http://dx.doi.org/10.5402/2012/383218.

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Many emerging applications are based on group communication model and many group communications like multimedia distribution and military applications require a security infrastructure that provides multiple levels of access control for group members. The group members are divided into a number of subgroups and placed at different privilege levels based on certain criteria. A member at higher level must be capable of accessing communication in its own level as well as its descendant lower levels but not vice versa. In this paper we propose a key management scheme for this multilayer group comm

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