scholarly journals L-S Categories of Simply-connected Compact Simple Lie Groups of Low Rank

2003 ◽  
pp. 199-212 ◽  
Author(s):  
Norio Iwase ◽  
Mamoru Mimura
Keyword(s):  
Lie Groups ◽  
Low Rank ◽  
Simple Lie Groups ◽  
Simply Connected

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 Almost paracontact and parahodge structures on manifolds

1985 ◽  
Vol 99 ◽  
pp. 173-187 ◽  
Author(s):  
Soji Kaneyuki ◽  
Floyd L. Williams
Keyword(s):  
Lie Groups ◽  
Geometric Quantization ◽  
Contact Structures ◽  
Simple Lie Groups ◽  
Coset Spaces ◽  
Adjoint Orbits ◽  
Simply Connected

In this paper we study the paracomplex analogues of almost contact structures, and we introduce and study the notion of parahodge structures on manifolds. In particular, we construct new examples of paracomplex manifolds and we find all simply connected parahermitian symmetric coset spaces, which are the adjoint orbits of noncompact simple Lie groups, with parahodge structures induced by the Killing forms. This is done by (i) observing that a version of the results of A. Morimoto [4] on almost contact structures can be formulated and proved for almost paracontact structures, and by (ii) the methods of geometric quantization [3] applied to parahermitian symmetric triples [1] in conjunction with results of [7]. Two of the main results are Theorem 2.5 (which ties together the above structures) and Corollary 3.9.

scholarly journals Lusternik–Schnirelmann category of non-simply connected compact simple Lie groups

2005 ◽  
Vol 150 (1-3) ◽  
pp. 111-123 ◽  
Author(s):  
Norio Iwase ◽  
Mamoru Mimura ◽  
Tetsu Nishimoto
Keyword(s):  
Lie Groups ◽  
Simple Lie Groups ◽  
Lusternik Schnirelmann ◽  
Simply Connected

The mod 2 homology of the space of loops on the exceptional Lie group

1989 ◽  
Vol 112 (3-4) ◽  
pp. 187-202 ◽  
Author(s):  
Akira Kono ◽  
Kazumuto Kozima
Keyword(s):  
Hopf Algebra ◽  
Lie Groups ◽  
Lie Group ◽  
Steenrod Algebra ◽  
Algebra Structure ◽  
Spectral Sequences ◽  
Hopf Algebra Structure ◽  
Simple Lie Groups ◽  
Simply Connected

SynopsisThe Hopf algebra structure of H*(ΩG, F2) and the action of the dual Steenrod algebra are completely and explicitly determined when G isone of the connected, simply connected, exceptional, simple Lie groups. The approach is homological, using connected coverings and spectral sequences.

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.

scholarly journals Twisted 6d (2, 0) SCFTs on a circle

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Zhihao Duan ◽  
Kimyeong Lee ◽  
June Nahmgoong ◽  
Xin Wang
Keyword(s):  
Lie Groups ◽  
Point Of View ◽  
Partition Functions ◽  
Congruence Subgroups ◽  
Gauge Groups ◽  
Simple Lie Groups ◽  
Instanton Contribution ◽  
Elliptic Genera ◽  
Supersymmetric Gauge ◽  
The One

Abstract We study twisted circle compactification of 6d (2, 0) SCFTs to 5d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting the 5d and 6d point of view respectively. The first is based on the blowup equations for the instanton partition function, from which in particular we determine explicitly the one-instanton contribution for all simple Lie groups. The second is based on the modular bootstrap program, and we propose a novel modular ansatz for the twisted elliptic genera that transform under the congruence subgroups Γ0(N) of SL(2, ℤ). We conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the genus one fibered Calabi-Yau threefolds, upon which one can determine the twisted elliptic genera recursively. We use our results to obtain the 6d Cardy formulas and find universal behaviour for all simple Lie groups. In addition, the Cardy formulas remain invariant under the twist once the normalization of the compact circle is taken into account.

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