scholarly journals Classification of Irreducible Holonomies of Torsion-Free Affine Connections

1999 ◽  
Vol 150 (1) ◽  
pp. 77 ◽  
Author(s):  
Sergei Merkulov ◽  
Lorenz Schwachhofer
Keyword(s):  
Affine Connections ◽  
Torsion Free

scholarly journals Classification of stable homotopy types with torsion-free homology

Topology ◽  
2001 ◽  
Vol 40 (4) ◽  
pp. 789-821 ◽  
Author(s):  
Hans-Joachim Baues ◽  
Yuri Drozd
Keyword(s):  
Stable Homotopy ◽  
Homotopy Types ◽  
Torsion Free

The classification of 2 and 3 torsion free polyhedra

2015 ◽  
Vol 31 (11) ◽  
pp. 1659-1682 ◽  
Author(s):  
Jian Zhong Pan ◽  
Zhong Jian Zhu
Keyword(s):  
Torsion Free

Exotic Holonomies ${\rm E}^{(a)}_7$

1997 ◽  
Vol 08 (05) ◽  
pp. 583-594 ◽  
Author(s):  
Quo-Shin Chi ◽  
Sergey Merkulov ◽  
Lorenz Schwachhöfer
Keyword(s):  
Symmetry Group ◽  
Lie Groups ◽  
Lie Group ◽  
Moduli Spaces ◽  
Local Symmetry ◽  
Positive Dimension ◽  
Affine Connections ◽  
Finite Dimensional ◽  
Torsion Free

It is proved that the Lie groups [Formula: see text] and [Formula: see text] represented in ℝ56 and the Lie group [Formula: see text] represented in ℝ112 occur as holonomies of torsion-free affine connections. It is also shown that the moduli spaces of torsion-free affine connections with these holonomies are finite dimensional, and that every such connection has a local symmetry group of positive dimension.

scholarly journals Rings with involution whose symmetric elements are central

1980 ◽  
Vol 3 (2) ◽  
pp. 247-253
Author(s):  
Taw Pin Lim
Keyword(s):  
Commutative Ring ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Bilinear Form ◽  
Semisimple Lie Algebra ◽  
Direct Sum ◽  
Rings With Involution ◽  
Torsion Free

In a ringRwith involution whose symmetric elementsSare central, the skew-symmetric elementsKform a Lie algebra over the commutative ringS. The classification of such rings which are2-torsion free is equivalent to the classification of Lie algebrasKoverSequipped with a bilinear formfthat is symmetric, invariant and satisfies[[x,y],z]=f(y,z)x−f(z,x)y. IfSis a field of char≠2,f≠0anddimK>1thenKis a semisimple Lie algebra if and only iffis nondegenerate. Moreover, the derived algebraK′is either the pure quaternions overSor a direct sum of mutually orthogonal abelian Lie ideals ofdim≤2.

scholarly journals Ioana's Superrigidity Theorem and Orbit Equivalence Relations

ISRN Algebra ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Samuel Coskey
Keyword(s):  
Ergodic Theory ◽  
Set Theory ◽  
Equivalence Relations ◽  
Orbit Equivalence ◽  
Borel Reducibility ◽  
Free Abelian Groups ◽  
Property T ◽  
Expository Paper ◽  
Torsion Free

We give a survey of Adrian Ioana's cocycle superrigidity theorem for profinite actions of Property (T) groups and its applications to ergodic theory and set theory in this expository paper. In addition to a statement and proof of Ioana's theorem, this paper features the following: (i) an introduction to rigidity, including a crash course in Borel cocycles and a summary of some of the best-known superrigidity theorems; (ii) some easy applications of superrigidity, both to ergodic theory (orbit equivalence) and set theory (Borel reducibility); and (iii) a streamlined proof of Simon Thomas's theorem that the classification of torsion-free abelian groups of finite rank is intractable.

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