Projective cocycles over SL(2,R) actions: measures invariant under the upper triangular group

Astérisque ◽  
2020 ◽  
Vol 415 ◽  
pp. 157-180 ◽  
Author(s):  
Christian BONATTI ◽  
Alex ESKIN ◽  
Amie WILKINSON
Keyword(s):  
Triangular Group

scholarly journals Tube domain and an orbit of a complex triangular group

2008 ◽  
Vol 259 (3) ◽  
pp. 697-711 ◽  
Author(s):  
Hideyuki Ishi ◽  
Takaaki Nomura
Keyword(s):  
Tube Domain ◽  
Triangular Group

scholarly journals The upper triangular group and operations in algebraic K-theory

Topology ◽  
2002 ◽  
Vol 41 (6) ◽  
pp. 1259-1275 ◽  
Author(s):  
Victor P. Snaith
Keyword(s):  
K Theory ◽  
Triangular Group

scholarly journals Anatomical study of Gerdy’s tubercle, its shape, texture and clinical application.

2020 ◽  
Vol 27 (05) ◽  
pp. 957-962
Author(s):  
Anwaar Hussain ◽  
Irfan Ahmed Mughal ◽  
Muhammad Hanif
Keyword(s):  
Anatomical Study ◽  
Common Peroneal Nerve ◽  
Left Tibia ◽  
Type Group ◽  
Safe Area ◽  
Group A ◽  
Group B ◽  
Gerdy’S Tubercle ◽  
Group D ◽  
Triangular Group

Objectives: The objective of this study is to lay emphasis on Gerdy’s tubercle, its morphology and clinical significance of Gerdy’s safe area in upper lateral part of tibia for any surgical intervention to avoid injury to neighboring common peroneal nerve. Study Design: Comparative anatomical study. Setting: Anatomy Department Faisalabad Medical University Faisalabad. Period: From 1st September 2018 to 20th Feb 2019. Material & Methods: Total 72 dried Pakistani tibia irrespective of sex (38 right and 34 left) were taken from the bone bank of Anatomy Department FMU. The upper end of tibia was studied with respect to the shape and texture of Gerdy’s tubercle. The shape is divided in to Group A having triangular, Group B oval, Group C irregular and group D unidentified in both right and left bones and their % age was calculated. Similarly the texture Of GT was divided in to Group A facet (smooth), Group B tubercle (rough) and Group C unidentified in both right and left tibia and then % age was calculated. Results: Total 72 dried human tibia were examined out of which 38 were of right side and rest 34 were of left side all showed presence of Gerdry’s tubercle. Regarding shape of GT Right tibia showed 12(31.5%) triangular (group A), Oval shape was 20 (52.6%) (Group B), number of irregular was 6 (15.9%) (Group C) and none unidentified (0%) (Group D). Regarding texture GT Right Tibia showed facet type Group A 16(42%), Group B 57% were of tubercle type (22) and non unidentified (Group D) Zero %. Total 34 left tibia Shape of GT was examined and found triangular (group A) in 18 tibia (52%) and oval shaped 6(17.6%) in group B. Whereas in group C 10 (29.4%). were irregular. The texture of left tibia 41.1% (14) were of facet Type Group A and 58.82% (20) were of tubercle type (group B). Total Number of Tibia (N=72) GT showed 41.6% triangular, 36.1% oval and 22.2% irregular. While 41.6% were facet and 58.3% tubercle in texture. Conclusion: This study concluded that the morphological study of Gerdy’s tubercle is mandatory to approach the lateral compartment of the knee joint for any surgical intervention. The calculation of safe area is so important to avoid injury to common peroneal nerve.

scholarly journals Combinatorial Hopf algebra of supercharacters of type D

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Carolina Benedetti
Keyword(s):  
Hopf Algebra ◽  
Finite Field ◽  
Type A ◽  
The Other ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
Type D ◽  
International Audience ◽  
Supercharacter Theory ◽  
Triangular Group

International audience We provide a Hopf algebra structure on the supercharacter theory for the unipotent upper triangular group of type {D} over a finite field. Also, we make further comments with respect to types {B} and {C}. Type {A} was explored by M. Aguiar et. al (2010), thus this extended abstract is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types. Dotamos con una estructura de álgebra de Hopf la teoría de supercaracteres del grupo de matrices unipotentes triangulares superiores de tipo{D} sobre un cuerpo finito. Ademas, discutimos brevemente los tipos {B} y {C}. El tipo A fue explorado por M. Aguiar et al (2010), por lo tanto este resumen extendido es una contribución para entender combinatoriamente la teoría de supercaracteres de los otros tipos de Lie clásicos. Nous construisons une structure d'algèbre de Hopf sur la thérie des supercharactères du groupe de matrices unipotentes triangulaires supéieures de type {D}. Nous donnons aussi quelques commentaires à l'égard des types {B} et {C} . Le type {A} a été explorée par M. Aguiar et al. (2010), donc ce résumé étendu est une contribution à la théorie combinatoire des supercharactères pour les autres types de Lie classiques. \par

TREE-WREATHING APPLIED TO GENERATION OF GROUPS BY FINITE AUTOMATA

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1205-1212 ◽  
Author(s):  
SAID SIDKI
Keyword(s):  
Wreath Product ◽  
Finite Index ◽  
Binary Tree ◽  
Infinite Sequence ◽  
Finite Automata ◽  
Residually Finite ◽  
Group Of Automorphisms ◽  
Triangular Group ◽  
Product Of Groups

We extend the tree-wreath product of groups introduced by Brunner and the author, as a generalization of the restricted wreath product, thus enlarging the class of groups known to be generated by finite synchronous automata. In particular, we prove that given a countable abelian residually finite 2 -group H and B = B(n,ℤ), a canonical subgroup of finite index in GL(n,ℤ), then the restricted wreath product H wr B can be generated by finite synchronous automata on 0,1. This is obtained by producing a representation of B as a group of automorphisms of the binary tree such that the stabilizer of the infinite sequence of 0's is trivial. The uni-triangular group U = U(n,ℤ) is a subgroup of B(n,ℤ) and so, H wr U also can be generated by finite synchronous automata on 0,1.

scholarly journals p-power conjugacy classes in U(n,q) and T(n,q)

2020 ◽  
pp. 2150121
Author(s):  
Silvio Dolfi ◽  
Anupam Singh ◽  
Manoj K. Yadav
Keyword(s):  
Algebraic Groups ◽  
Recursive Formula ◽  
Conjugacy Classes ◽  
Image Size ◽  
Large Size ◽  
Power Maps ◽  
Unitriangular Group ◽  
Triangular Group

Let [Formula: see text] be a [Formula: see text]-power where [Formula: see text] is a fixed prime. In this paper, we look at the [Formula: see text]-power maps on unitriangular group [Formula: see text] and triangular group [Formula: see text]. In the spirit of Borel dominance theorem for algebraic groups, we show that the image of this map contains large size conjugacy classes. For the triangular group we give a recursive formula to count the image size.

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