scholarly journals Unimodular group matrices with rational integers as elements

1964 ◽  
Vol 14 (2) ◽  
pp. 719-726 ◽  
Author(s):  
Robert Thompson
Keyword(s):  
Unimodular Group ◽  
Group Matrices

scholarly journals Resultants and group matrices

1980 ◽  
Vol 33 ◽  
pp. 111-122 ◽  
Author(s):  
Kai Wang
Keyword(s):  
Group Matrices

scholarly journals On the classification of isotropic tensors

1987 ◽  
Vol 29 (2) ◽  
pp. 185-196 ◽  
Author(s):  
P. G. Appleby ◽  
B. R. Duffy ◽  
R. W. Ogden
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Final Section ◽  
Complete Classification ◽  
Coordinate Transformations ◽  
Tensor Fields ◽  
Isotropic Tensor ◽  
Unimodular Group ◽  
Derivatives Of

A tensor is said to be isotropic relative to a group of transformations if its components are invariant under the associated group of coordinate transformations. In this paper we review the classification of tensors which are isotropic under the general linear group, the special linear (unimodular) group and the rotational group. These correspond respectively to isotropic absolute tensors [4, 8] isotropic relative tensors [4] and isotropic Cartesian tensors [3]. New proofs are given for the representation of isotropic tensors in terms of Kronecker deltas and alternating tensors. And, for isotropic Cartesian tensors, we provide a complete classification, clarifying results described in [3].In the final section of the paper certain derivatives of isotropic tensor fields are examined.

scholarly journals DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS

2014 ◽  
Vol 57 (3) ◽  
pp. 693-707
Author(s):  
YEMON CHOI
Keyword(s):  
Invertible Element ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Complex Line ◽  
Locally Compact ◽  
The Real ◽  
C Algebra ◽  
Finite Algebras ◽  
Unimodular Group ◽  
Reduced Group

AbstractAn algebraAis said to be directly finite if each left-invertible element in the (conditional) unitization ofAis right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras ofp-pseudofunctions, showing that these algebras are directly finite ifGis amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply thatL1(G) is not directly finite whenGis the affine group of either the real or complex line.

scholarly journals Two-element generation of the projective unimodular group

1959 ◽  
Vol 3 (3) ◽  
pp. 421-439 ◽  
Author(s):  
A. A. Albert ◽  
John Thompson
Keyword(s):  
Unimodular Group

scholarly journals Automorphisms of the Gaussian unimodular group

1958 ◽  
Vol 87 (1) ◽  
pp. 76-76 ◽  
Author(s):  
Joseph Landin ◽  
Irving Reiner
Keyword(s):  
Unimodular Group

The Betti Numbers of the Simple Lie Groups

1958 ◽  
Vol 10 ◽  
pp. 349-356 ◽  
Author(s):  
A. J. Coleman
Keyword(s):  
Lie Groups ◽  
Orthogonal Group ◽  
Betti Numbers ◽  
Algebraic Methods ◽  
Classical Groups ◽  
Compact Lie Groups ◽  
Poincaré Polynomial ◽  
Unimodular Group ◽  
Simple Lie Groups

The purpose of the present paper1 is to simplify the calculation of the Betti numbers of the simple compact Lie groups. For the unimodular group and the orthogonal group on a space of odd dimension the form of the Poincaré polynomial was correctly guessed by E. Cartan in 1929 (5, p. 183). The proof of his conjecture and its extension to the four classes of classical groups was given by L. Pontrjagin (13) using topological arguments and then by R. Brauer (2) using algebraic methods.

scholarly journals On a representation of the automorphism group of a graph in a unimodular group

2021 ◽  
Vol 344 (12) ◽  
pp. 112606
Author(s):  
István Estélyi ◽  
Ján Karabáš ◽  
Roman Nedela ◽  
Alexander Mednykh
Keyword(s):  
Automorphism Group ◽  
Unimodular Group
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