Explicit construction of nontrivial elements for homotopy groups of classical Lie groups

1990 ◽  
Vol 31 (6) ◽  
pp. 1494-1502 ◽  
Author(s):  
Albert T. Lundell ◽  
Yasunari Tosa
Keyword(s):  
Lie Groups ◽  
Explicit Construction ◽  
Homotopy Groups

scholarly journals Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class

2014 ◽  
Vol 14 (2) ◽  
pp. 247-272 ◽  
Author(s):  
Antti J. Harju ◽  
Jouko Mickelsson
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lie Groups ◽  
Explicit Construction ◽  
Theory Model ◽  
Quantum Field ◽  
Compact Lie Groups ◽  
Field Theory Model ◽  
Cup Product ◽  
K Theory

AbstractTwisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral one form on and an integral class in H2(M,ℤ). This case was studied some time ago by V. Mathai, R. Melrose, and I.M. Singer. Our aim is to give an explicit construction for the twisted K-theory classes using a quantum field theory model, in the same spirit as the supersymmetric Wess-Zumino-Witten model is used for constructing (equivariant) twisted K-theory classes on compact Lie groups.

scholarly journals ON LIE GROUPS, CLUSTER VARIABLES AND INTEGRABLE SYSTEMS

2013 ◽  
Vol 28 (03n04) ◽  
pp. 1340007
Author(s):  
A. MARSHAKOV
Keyword(s):  
Lie Groups ◽  
Integrable Systems ◽  
Explicit Construction ◽  
Integrable Models ◽  
Loop Groups ◽  
Integrals Of Motion ◽  
General Terms

We propose an explicit construction for the integrable models on Poisson submanifolds of the Lie groups. The integrals of motion are computed in cluster variables via the Lax map. This generalized construction for the co-extended loop groups allows to formulate, in general terms, some new classes of integrable models.

v 1 -Periodic Homotopy Groups of Exceptional Lie Groups: Torsion-Free Cases

1992 ◽  
Vol 333 (1) ◽  
pp. 115 ◽  
Author(s):  
Martin Bendersky ◽  
Donald M. Davis ◽  
Mamoru Mimura
Keyword(s):  
Lie Groups ◽  
Homotopy Groups ◽  
Exceptional Lie Groups ◽  
Torsion Free

scholarly journals Homotopy groups of the spaces of self-maps of lie groups II

2009 ◽  
Vol 32 (3) ◽  
pp. 530-546
Author(s):  
Katsumi Ōshima ◽  
Hideaki Ōshima
Keyword(s):  
Lie Groups ◽  
Homotopy Groups
Sign in / Sign up

Export Citation Format

Share Document