scholarly journals The Representation Ring of a Simply Connected Lie Group as a λ-Ring

2007 ◽  
Vol 35 (3) ◽  
pp. 875-883 ◽  
Author(s):  
Pierre Guillot
Keyword(s):  
Lie Group ◽  
Representation Ring ◽  
Simply Connected ◽  
Connected Lie Group

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

LEFT INVARIANT COMPLEX STRUCTURES ON NILPOTENT SIMPLY CONNECTED INDECOMPOSABLE 6-DIMENSIONAL REAL LIE GROUPS

2007 ◽  
Vol 17 (01) ◽  
pp. 115-139 ◽  
Author(s):  
L. MAGNIN
Keyword(s):  
Automorphism Group ◽  
Normal Form ◽  
Lie Groups ◽  
Lie Algebras ◽  
Lie Group ◽  
Normal Forms ◽  
Equivalence Classes ◽  
Complex Structures ◽  
Simply Connected ◽  
Connected Lie Group

Integrable complex structures on indecomposable 6-dimensional nilpotent real Lie algebras have been computed in a previous paper, along with normal forms for representatives of the various equivalence classes under the action of the automorphism group. Here we go to the connected simply connected Lie group G0 associated to such a Lie algebra 𝔤. For each normal form J of integrable complex structures on 𝔤, we consider the left invariant complex manifold G = (G0, J) associated to G0 and J. We explicitly compute a global holomorphic chart for G and we write down the multiplication in that chart.

Self-Maps of Low Rank Lie Groups at Odd Primes

2010 ◽  
Vol 62 (2) ◽  
pp. 284-304 ◽  
Author(s):  
Jelena Grbić ◽  
Stephen Theriault
Keyword(s):  
Lie Groups ◽  
Structural Properties ◽  
Lie Group ◽  
Low Rank ◽  
Rank Condition ◽  
Homotopy Classes ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a simple, compact, simply-connected Lie group localized at an odd prime p. We study the group of homotopy classes of self-maps [G, G] when the rank of G is low and in certain cases describe the set of homotopy classes ofmultiplicative self-maps H[G, G]. The low rank condition gives G certain structural properties which make calculations accessible. Several examples and applications are given.

scholarly journals Strictification of étale stacky Lie groups

2011 ◽  
Vol 148 (3) ◽  
pp. 807-834 ◽  
Author(s):  
Giorgio Trentinaglia ◽  
Chenchang Zhu
Keyword(s):  
Fundamental Group ◽  
Lie Groups ◽  
Lie Algebra ◽  
Lie Group ◽  
Crossed Module ◽  
Simply Connected ◽  
The Given ◽  
Connected Lie Group

AbstractWe define stacky Lie groups to be group objects in the 2-category of differentiable stacks. We show that every connected and étale stacky Lie group is equivalent to a crossed module of the form (Γ,G) where Γ is the fundamental group of the given stacky Lie group and G is the connected and simply connected Lie group integrating the Lie algebra of the stacky group. Our result is closely related to a strictification result of Baez and Lauda.

Symmetries of the Quantum State Space and Group Representations

1998 ◽  
Vol 10 (07) ◽  
pp. 893-924 ◽  
Author(s):  
Gianni Cassinelli ◽  
Ernesto de Vito ◽  
Pekka Lahti ◽  
Alberto Levrero
Keyword(s):  
State Space ◽  
Quantum System ◽  
Symmetry Group ◽  
Quantum State ◽  
Lie Group ◽  
Universal Covering ◽  
Unitary Representations ◽  
Group Representations ◽  
Simply Connected ◽  
Connected Lie Group

The homomorphisms of a connected Lie group G into the symmetry group of a quantum system are classified in terms of unitary representations of a simply connected Lie group associated with G. Moreover, an explicit description of the T-multipliers of G is obtained in terms of the ℝ-multipliers of the universal covering G* of G and the characters of G*. As an application, the Poincaré group and the Galilei group, both in 3+1 and 2+1 dimensions, are considered.

scholarly journals Conformal Killing forms on 2-step nilpotent Riemannian Lie groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Viviana del Barco ◽  
Andrei Moroianu
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Group ◽  
Conformal Killing ◽  
Nilpotent Lie Groups ◽  
Killing Form ◽  
Invariant Metric ◽  
Nilpotent Lie Algebra ◽  
Simply Connected ◽  
Connected Lie Group

Abstract We study left-invariant conformal Killing 2- or 3-forms on simply connected 2-step nilpotent Riemannian Lie groups. We show that if the center of the group is of dimension greater than or equal to 4, then every such form is automatically coclosed (i.e. it is a Killing form). In addition, we prove that the only Riemannian 2-step nilpotent Lie groups with center of dimension at most 3 and admitting left-invariant non-coclosed conformal Killing 2- and 3-forms are the following: The Heisenberg Lie groups and their trivial 1-dimensional extensions, endowed with any left-invariant metric, and the simply connected Lie group corresponding to the free 2-step nilpotent Lie algebra on 3 generators, with a particular 1-parameter family of metrics. The explicit description of the space of conformal Killing 2- and 3-forms is provided in each case.

scholarly journals THE RADIAL PART OF THE ZERO-MODE HAMILTONIAN FOR SIGMA MODELS WITH GROUP TARGET SPACE

2004 ◽  
Vol 16 (05) ◽  
pp. 603-628 ◽  
Author(s):  
DOUG PICKRELL
Keyword(s):  
Sigma Models ◽  
Lie Group ◽  
Sigma Model ◽  
Zero Mode ◽  
Target Space ◽  
Two Dimensional ◽  
Radial Part ◽  
Group Target ◽  
Simply Connected ◽  
Connected Lie Group

In this note, we use geometric arguments to derive a possible form for the radial part of the "zero-mode Hamiltonian" for the two-dimensional sigma model with target space S3, or more generally a compact simply connected Lie group.

scholarly journals Homotopy Groups of Compact Lie Groups E6, E7 and E8

1968 ◽  
Vol 32 ◽  
pp. 109-139 ◽  
Author(s):  
Hideyuki Kachi
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Characteristic Zero ◽  
Exterior Algebra ◽  
Homotopy Groups ◽  
Compact Lie Groups ◽  
Simply Connected ◽  
Connected Lie Group

Let G be a simple, connected, compact and simply-connected Lie group. If k is the field with characteristic zero, then the algebra of cohomology H*(G ; k) is the exterior algebra generated by the elements x1, …, xl of the odd dimension n1, …, nl; the integer l is the rank of G and is the dimension of G.

scholarly journals Integrating -algebras

2008 ◽  
Vol 144 (4) ◽  
pp. 1017-1045 ◽  
Author(s):  
André Henriques
Keyword(s):  
Lie Algebra ◽  
Lie Group ◽  
Explicit Construction ◽  
Classifying Space ◽  
Simply Connected ◽  
Work Done ◽  
Connected Lie Group

AbstractGiven a Lie n-algebra, we provide an explicit construction of its integrating Lie n-group. This extends work done by Getzler in the case of nilpotent $L_\infty $-algebras. When applied to an ordinary Lie algebra, our construction yields the simplicial classifying space of the corresponding simply connected Lie group. In the case of the string Lie 2-algebra of Baez and Crans, we obtain the simplicial nerve of their model of the string group.

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