scholarly journals On Invariant Operations on a Manifold with a Linear Connection and an Orientation

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2577
Author(s):  
Adrián Gordillo-Merino ◽  
Raúl Martínez-Bohórquez ◽  
José Navarro-Garmendia
Keyword(s):  
Linear Group ◽  
Linear Connection ◽  
Special Linear Group ◽  
Bianchi Identities ◽  
Special Linear ◽  
Linear Representations ◽  
Natural Operators

We prove a theorem that describes all possible tensor-valued natural operations in the presence of a linear connection and an orientation in terms of certain linear representations of the special linear group. As an application of this result, we prove a characterization of the torsion and curvature operators as the only natural operators that satisfy the Bianchi identities.

scholarly journals A further characterization of a projective special linear group

1977 ◽  
Vol 24 (1) ◽  
pp. 112-116 ◽  
Author(s):  
Saad Adnan
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Projective Special Linear Group ◽  
Special Linear

AbstractIn this paper we present a characterization of PSL(2,7) by a condition different from that given in our previous paper.

scholarly journals Integral cohomology and Chern classes of the special linear group over the ring of integers

2001 ◽  
Vol 131 (3) ◽  
pp. 445-457
Author(s):  
DOMINIQUE ARLETTAZ ◽  
CHRISTIAN AUSONI ◽  
MAMORU MIMURA ◽  
NOBUAKI YAGITA
Keyword(s):  
Linear Group ◽  
Upper Bound ◽  
Special Linear Group ◽  
Discrete Groups ◽  
Chern Classes ◽  
Additive Structure ◽  
Special Linear ◽  
Ring Of Integers ◽  
Integral Cohomology ◽  
Complete Calculation

This paper is devoted to the complete calculation of the additive structure of the 2-torsion of the integral cohomology of the infinite special linear group SL(ℤ) over the ring of integers ℤ. This enables us to determine the best upper bound for the order of the Chern classes of all integral and rational representations of discrete groups.

scholarly journals The third homology of the special linear group of a field

2009 ◽  
Vol 213 (9) ◽  
pp. 1665-1680 ◽  
Author(s):  
Kevin Hutchinson ◽  
Liqun Tao
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Special Linear ◽  
The Third

On the existence of Engel pairs in certain linear groups

2016 ◽  
Vol 15 (04) ◽  
pp. 1650062
Author(s):  
S. G. Quek ◽  
K. B. Wong ◽  
P. C. Wong
Keyword(s):  
Linear Group ◽  
Field Extension ◽  
Special Linear Group ◽  
Linear Groups ◽  
Special Linear

Let [Formula: see text] be a group and [Formula: see text]. The 2-tuple [Formula: see text] is said to be an [Formula: see text]-Engel pair, [Formula: see text], if [Formula: see text], [Formula: see text] and [Formula: see text]. Let SL[Formula: see text] be the special linear group of degree [Formula: see text] over the field [Formula: see text]. In this paper, we show that given any field [Formula: see text], there is a field extension [Formula: see text] of [Formula: see text] with [Formula: see text] such that SL[Formula: see text] has an [Formula: see text]-Engel pair for some integer [Formula: see text]. We will also show that SL[Formula: see text] has a [Formula: see text]-Engel pair if [Formula: see text] is a field of characteristic [Formula: see text].

scholarly journals The special linear group for nonassociative rings

2020 ◽  
Vol 23 (2) ◽  
pp. 327-335
Author(s):  
Harry Petyt
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Large Classes ◽  
Special Linear ◽  
Lie Ring ◽  
Definition Of ◽  
Associative Rings

AbstractWe extend to arbitrary rings a definition of the octonion special linear group due to Baez. At the infinitesimal level, we get a Lie ring, which we describe over some large classes of rings, including all associative rings and all algebras over a field. As a corollary, we compute all the groups Baez defined.

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