User user20369 - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T16:41:48Z http://mathoverflow.net/feeds/user/20369 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/94860/lie-algebra-for-a-general-group "Lie algebra" for a general group ? user20369 2012-04-22T17:39:13Z 2012-06-22T00:58:22Z <p>Is there analog of Lie algebra for the case of topological groups which are not necessarily differentiable manifolds, and in particular for finite groups? here by "analog" i mean that it should have similar kind of relations to given group as of a finite dimensional Lie algebra with its corresponding Lie group. for example there should be some analog of "Exponential map"; Every linear representation of group should also be a linear representation of its algebra, and this should be in some sense compatible with the exponential map between the two; etc</p> <p>thanks,</p> http://mathoverflow.net/questions/84930/covariant-derivative Covariant derivative user20369 2012-01-05T05:14:38Z 2012-01-05T06:08:22Z <p>Hi, Is it true that covariant derivative on any vector bundle over a manifold X comes from some connection on the bundle of linear frames of that vector bundle? This statement is true for the case of tangent bundle, but I am not sure if it is true in general or not. If it is true then can someone please suggest some reference for its proof.</p> http://mathoverflow.net/questions/88978/convergence-of-analytic-covering-maps-to-a-covering-map/89434#89434 Comment by user20369 user20369 2012-08-05T08:26:47Z 2012-08-05T08:26:47Z Thanks a lot :) http://mathoverflow.net/questions/88978/convergence-of-analytic-covering-maps-to-a-covering-map/89434#89434 Comment by user20369 user20369 2012-08-05T06:59:30Z 2012-08-05T06:59:30Z Misha can you please tell some reference(s) regarding your second argument (general one). http://mathoverflow.net/questions/102537/representations-of-the-lorentz-group-in-4-dimensions Comment by user20369 user20369 2012-07-18T19:47:53Z 2012-07-18T19:47:53Z Notation used here is somewhat confusing. You can rather understand it like this : Take two copies of su(2) algebra. Denote their generators as $A_1,A_2,A_3$ and $B_1,B_2,B_3$ respectively, which thus satisfy relations : $[A_i,A_j]=i\epsilon_{ijk} A_k$ (sum over k), and similarly for $B_i$'s. Now let $V$ be a representation space for the first copy of su(2), and $W$ be a representation space for the second copy of su(2). Form the tensor product $V\otimes W$, and define action of lorentz algebra on it as : $J_i=A_i\otimes I+I\otimes B_i$, and $K_i=i(A_i\otimes I-I\otimes B_i)$. http://mathoverflow.net/questions/94860/lie-algebra-for-a-general-group/94869#94869 Comment by user20369 user20369 2012-04-22T20:39:40Z 2012-04-22T20:39:40Z Thanks for your answer, http://mathoverflow.net/questions/94860/lie-algebra-for-a-general-group/94870#94870 Comment by user20369 user20369 2012-04-22T20:38:23Z 2012-04-22T20:38:23Z Thank you Marc, http://mathoverflow.net/questions/94860/lie-algebra-for-a-general-group Comment by user20369 user20369 2012-04-22T20:32:20Z 2012-04-22T20:32:20Z @ Qiaochu Yuan. Anything like a Lie group :-) http://mathoverflow.net/questions/94860/lie-algebra-for-a-general-group/94870#94870 Comment by user20369 user20369 2012-04-22T20:23:55Z 2012-04-22T20:23:55Z Can you please suggest some reference(s) where this projective limit relation between almost connected, locally compact groups and Lie groups has been explained/studied/used. http://mathoverflow.net/questions/84930/covariant-derivative/84933#84933 Comment by user20369 user20369 2012-01-05T06:33:11Z 2012-01-05T06:33:11Z thanks for the answer and for the reference. http://mathoverflow.net/questions/84930/covariant-derivative/84932#84932 Comment by user20369 user20369 2012-01-05T06:30:55Z 2012-01-05T06:30:55Z thanks for the references.