Tag: lie-algebras

90 Has the Lie group E8 really been detected experimentally? 2010-07-17T21:34:07.500

89 why study Lie algebras? 2011-03-17T00:24:39.930

65 What would you want on a Lie theory cheat poster? 2011-04-26T13:57:08.153

56 Surprisingly short or elegant proofs using Lie theory 2017-04-04T19:22:45.497

55 What is the symbol of a differential operator? 2009-10-30T22:12:06.547

49 Is "semisimple" a dense condition among Lie algebras? 2009-12-24T07:41:14.673

44 What is significant about the half-sum of positive roots? 2011-11-05T20:53:57.463

44 Beautiful descriptions of exceptional groups 2012-06-15T19:00:07.217

40 What does the generating function $x/(1 - e^{-x})$ count? 2009-12-18T01:44:01.313

38 Why the Killing form? 2010-07-19T23:03:32.723

37 What algebraic group does Tannaka-Krein reconstruct when fed the category of modules of a non-algebraic Lie algebra? 2010-04-15T04:06:49.823

37 Implications of non-negativity of coefficients of arbitrary Kazhdan-Lusztig polynomials? 2012-11-18T00:35:04.247

36 What role does the "dual Coxeter number" play in Lie theory (and should it be called the "Kac number")? 2010-05-22T17:52:20.040

33 Roadmap to Geometric Representation Theory (leading to Langlands)? 2016-04-11T18:50:14.637

32 Is every finite-dimensional Lie algebra the Lie algebra of an algebraic group? 2009-10-05T19:48:00.190

32 Why is there a connection between enumerative geometry and nonlinear waves? 2013-10-22T17:15:27.950

32 Is there a geometric construction of hyperbolic Kac-Moody groups? 2016-03-04T16:48:56.607

30 Motivating the Casimir element 2011-09-06T21:47:38.067

29 "Modern" proof for the Baker-Campbell-Hausdorff formula 2012-06-10T11:14:03.417

28 Nice proofs of the Poincaré–Birkhoff–Witt theorem 2012-02-03T05:41:51.017

26 Why is Lie's Third Theorem difficult? 2009-12-13T19:31:56.677

26 Why should affine lie algebras and quantum groups have equivalent representation theories? 2014-07-31T14:48:25.277

26 Why do the adjoint representations of three exceptional groups have the same first eight moments? 2016-02-20T15:10:05.433

25 Cohomology of Lie groups and Lie algebras 2010-01-13T22:17:32.740

25 Does the quantum subgroup of quantum su_2 called E_8 have anything at all to do with the Lie algebra E_8? 2010-07-19T01:06:57.553

25 Isometry group of a homogeneous space 2011-09-18T12:25:43.957

25 A mysterious Heisenberg algebra identity from Sylvester, 1867 2012-07-15T11:12:00.903

25 Why do Lie algebras pop up, from a categorical point of view? 2014-07-25T08:34:29.713

24 Learning about Lie groups 2009-09-28T19:41:13.933

24 What was Casimir's precise role in describing the center of the universal enveloping algebra of a semisimple Lie algebra? 2010-10-05T13:40:21.200

24 Is the sequence of partition numbers log-concave? 2013-08-01T15:18:29.610

24 Follow-up to Steinberg's problem (12) in his 1966 ICM talk? 2016-07-18T20:24:07.893

23 What's the status of the following relationship between Ramanujan's $\tau$ function and the simple Lie algebras? 2009-12-24T23:48:46.777

21 How are these two ways of thinking about the cross product related? 2010-07-30T07:13:55.153

21 Pythagorean 5-tuples 2011-04-24T09:14:09.013

21 When is a finite dimensional real or complex Lie Group not a matrix group 2011-05-07T14:02:23.740

21 Why the BGG category O? 2011-05-13T20:26:15.770

20 "isotropic" subspaces of a simple Lie algebra 2009-10-25T17:50:38.683

20 Formal Geometry 2009-11-19T03:16:14.307

20 Automorphism group of real orthogonal Lie groups 2016-04-09T12:43:40.137

20 Curious fact about number of roots of $\mathfrak{sl}_n$ 2017-05-13T01:29:50.093

19 Number of triples of roots (of a simply-laced root system) which sum to zero 2011-05-26T23:07:33.007

18 What is the Zariski closure of the space of semisimple Lie algebras? 2009-12-25T01:06:33.500

18 Outer automorphisms of simple Lie Algebras 2010-02-09T03:31:21.120

18 Lie algebra automorphisms and detecting knot orientation by Vassiliev invariants 2010-08-27T02:20:28.893

18 On a drawing in Dixmier's Enveloping Algebras 2015-03-23T16:20:41.833

18 What is the homomorphism between the third exterior and third symmetric power of the adjoint representation of a simple Lie algebra? 2015-08-05T13:06:04.043

18 What happened to the fourth paper in the series "On the classification of primitive ideals for complex classical Lie algebras" by Garfinkle? 2015-11-10T07:47:57.823

17 Generators of the cohomology of a Lie algebra 2010-12-17T16:35:47.267

17 homotopy type of connected Lie groups 2011-01-24T16:49:45.873

17 Invariants for the exceptional complex simple Lie algebra $F_4$ 2012-05-06T18:10:59.720

17 Is homology finitely generated as an algebra? 2014-10-03T03:24:28.203

17 Does there exist something like an $H_3$ and $H_4$ (icosahedral) Lie algebra or algebraic group? 2016-08-17T13:25:27.640

16 Introduction to W-Algebras/Why W-algebras? 2010-01-01T22:09:25.353

16 Matrix representation for $F_4$ 2010-02-26T04:07:34.233

16 Combinatorial identity involving the Coxeter numbers of root systems 2010-09-16T16:47:55.000

16 How do I stop worrying about root systems and decomposition theorems (for reductive groups)? 2010-10-20T20:48:28.903

16 Gap in an argument in Fulton & Harris? 2011-02-06T20:17:32.260

16 (Dis)similarity between groups and Lie algebras 2011-06-20T04:56:22.563

16 Is a retract of a free object free? 2012-03-09T17:17:56.073

16 Motivation of Virasoro algebra 2012-12-26T23:37:33.753

16 Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group? 2016-01-07T11:00:03.163

16 Are the unipotent and nilpotent varieties isomorphic in bad characteristics? 2017-05-02T14:14:32.003

15 Modern reference for maximal connected subgroups of compact Lie groups 2011-04-01T19:42:17.397

15 Why do sl(2) and so(3) correspond to different points on the Vogel plane? 2011-05-04T19:19:00.707

15 Can one show the equivalence of the abstract and classical Jordan decompositions for simple Lie algebras without complete reducibility? 2013-09-15T00:33:12.127

15 Lie algebras vs. graph complexes 2013-12-15T21:22:11.343

15 factorization of the regular representation of the symmetric group 2016-01-02T22:57:07.053

14 Folding by Automorphisms 2009-11-03T02:11:23.030

14 Is every finite-dimensional Lie algebra the Lie algebra of a closed linear Lie group? 2009-12-01T23:43:20.270

14 Understanding moment maps and Lie brackets 2010-02-06T20:03:23.447

14 What is the physical meaning of a Lie algebra symmetry? 2010-05-17T05:19:22.533

14 Is every G-invariant function on a Lie algebra a trace? 2010-05-21T00:06:41.840

14 Basis-free definition of Casimir element? 2011-01-20T06:53:22.040

14 Proof for which primes H*G has torsion 2012-06-14T02:16:35.763

14 What is a Homotopy between $L_\infty$-algebra morphisms 2013-08-11T16:52:53.747

14 "Special" meanders 2013-11-03T09:50:16.393

14 Associators, Grothendieck-Teichmüller group and monoidal categories 2014-01-02T21:49:13.203

14 Examples of representations of quantum groups 2017-10-05T17:54:39.417

13 What does the nilpotent cone represent? 2010-01-08T17:41:47.973

13 What is the recent development of D-module and representation theory of Kac-Moody algebra? 2010-02-09T12:32:45.973

13 Polynomial invariants of the exceptional Weyl groups 2010-09-03T11:35:08.780

13 Deformations of semisimple Lie algebras 2010-11-26T18:42:08.527

13 Torsion for Lie algebras and Lie groups 2011-06-04T03:37:20.340

13 For $\mathfrak g$ A Lie algebra of type $ E_7 $, $\mathfrak h $ a Cartan subalgebra and $\Delta$ the resulting root system, does $ Aut(\mathfrak g,\mathfrak h)\rightarrow Aut(\Delta) $ split over the Weyl group? 2011-07-14T12:31:15.503

13 So, did Poincaré prove PBW or not? 2011-09-08T19:12:23.647

13 Ternary "Lie structure" 2012-05-10T16:21:14.160

13 About the intrinsic definition of the Weyl group of complex semisimple Lie algebras 2012-08-02T02:10:29.030

13 Deligne's 1996 note on exceptional Lie groups 2013-01-10T13:57:14.327

13 decompositions for exceptional Lie algebras $E_6$, $E_7$ and $E_8$ 2013-01-17T16:58:32.247

13 Characteristic subgroup of nilpotent group that is not invariant under powering 2013-03-12T07:16:48.117

13 Why are affine Lie algebras called affine? 2013-05-19T00:24:05.467

13 Is this error in this paper of Langlands fixable? 2013-10-09T21:13:31.880

13 Intuition for the Cartan connection and "rolling without slipping" in Cartan geometry 2016-01-28T23:39:35.727

13 Free groups and free restricted Lie algebras 2017-02-03T19:49:58.383

13 Constructing $E_8$ from its branching to $A_8$ 2017-06-13T14:22:05.727

13 Can one define quantized universal enveloping algebras in a basis-free way? 2017-07-19T19:28:54.367

13 Is there a simple system that has $\text{SU}(3)$ symmetry? 2017-10-30T20:39:57.340

12 Matrices into path algebras 2009-10-26T22:16:44.997