scholarly journals Spectral isolation of bi-invariant metrics on compact Lie groups

2010 ◽  
Vol 60 (5) ◽  
pp. 1617-1628 ◽  
Author(s):  
Carolyn S. Gordon ◽  
Dorothee Schueth ◽  
Craig J. Sutton
Keyword(s):  
Lie Groups ◽  
Invariant Metrics ◽  
Compact Lie Groups

scholarly journals Invariant Metrics with Nonnegative Curvature on Compact Lie Groups

2007 ◽  
Vol 50 (1) ◽  
pp. 24-34 ◽  
Author(s):  
Nathan Brown ◽  
Rachel Finck ◽  
Matthew Spencer ◽  
Kristopher Tapp ◽  
Zhongtao Wu
Keyword(s):  
Sectional Curvature ◽  
Lie Groups ◽  
Nonnegative Curvature ◽  
Invariant Metrics ◽  
Compact Lie Groups ◽  
Nonnegative Sectional Curvature ◽  
Left Invariant Metrics

AbstractWe classify the left-invariant metrics with nonnegative sectional curvature on SO(3) and U(2).

New non-naturally reductive Einstein metrics on SO(n)

2018 ◽  
Vol 29 (11) ◽  
pp. 1850083 ◽  
Author(s):  
Bo Zhang ◽  
Huibin Chen ◽  
Ju Tan
Keyword(s):  
Lie Groups ◽  
Ricci Tensor ◽  
Einstein Metrics ◽  
Gröbner Bases ◽  
Invariant Metrics ◽  
Polynomial Equations ◽  
Compact Lie Groups ◽  
Symbolic Computations ◽  
Left Invariant Metrics ◽  
Naturally Reductive

We obtain new invariant Einstein metrics on the compact Lie groups [Formula: see text] ([Formula: see text]) which are not naturally reductive. This is achieved by imposing certain symmetry assumptions in the set of all left-invariant metrics on [Formula: see text] and by computing the Ricci tensor for such metrics. The Einstein metrics are obtained as solutions of systems polynomial equations, which we manipulate by symbolic computations using Gröbner bases.

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.

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