User xuanting cai - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T08:18:21Z http://mathoverflow.net/feeds/user/12445 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/94712/primary-decomposition-theorem-in-quantum-torus primary decomposition theorem in quantum torus Xuanting Cai 2012-04-21T06:13:32Z 2012-04-21T06:13:32Z <p>Hi, I am wondering whether there is primary decomposition theorem in quantum torus.</p> <p>Thanks</p> http://mathoverflow.net/questions/62145/recursion-formula-for-odd-holonomic-function recursion formula for odd holonomic function Xuanting Cai 2011-04-18T16:04:26Z 2011-05-08T21:36:47Z <p>suppose we have a map $f:\mathbb{Z}\longrightarrow\mathbb{C}[t^{\pm}]$ with property that $f(i)=-f(-i)$.</p> <p>The algebra $\mathcal{T}=\mathbb{C}[t^{\pm}][L^{\pm},M^{\pm}]/[LM=tML]$ acts on $f$ by $(Lf)(i)=f(i+1),(Mf)(i)=t^if(i)$.</p> <p>Should the annihilating ideal of $f$ generated by annihilators in symmetric part of $\mathcal{T}$?</p> <p>Symmetric part means the subset with all element like $aL^xM^y+aL^{-x}M^{-y}$ and their multiplication or linear combination.</p> <p>Thanks.</p> http://mathoverflow.net/questions/54496/what-is-the-definition-of-algebro-gemetric-quotient What is the definition of algebro-gemetric quotient? Xuanting Cai 2011-02-06T05:30:57Z 2011-02-06T10:50:19Z <p>If there a group G acting on a variety V. The action is algebraic. What is the definition of algebro-geometric quotient of this action?</p> <p>I hope you can give a very basic explanation.</p> <p>Thanks.</p> http://mathoverflow.net/questions/53514/seiberg-witten-equation-on-s2-times-s1 Seiberg-Witten equation on S^2\times S^1 Xuanting Cai 2011-01-27T17:39:00Z 2011-01-27T18:49:37Z <p>What are the irreducible solutions of Seiberg-Witten equation on S^2\times S^1? Thanks.</p> http://mathoverflow.net/questions/53314/why-must-a-reducible-flat-su2-connection-over-a-homology-sphere-be-trivial Why must a reducible flat SU(2)-connection over a homology sphere be trivial? Xuanting Cai 2011-01-26T04:06:21Z 2011-01-26T14:13:59Z <p>Let $M$ be a homology sphere. Suppose $P=M\times SU(2)$ is the trivial $SU(2)$ principal bundle. Let $R$ be all reducible connections on $P$. Here $A$ in $R$ is reducible if the gauge transformation group acting on $A$ has nontrivial stable subgroup. I want to see that the only flat connection in $R$ is the product connection.</p> http://mathoverflow.net/questions/62145/recursion-formula-for-odd-holonomic-function Comment by Xuanting Cai Xuanting Cai 2011-05-28T22:18:12Z 2011-05-28T22:18:12Z C[t^{\pm}] means the Laurant Polynomials of t http://mathoverflow.net/questions/62145/recursion-formula-for-odd-holonomic-function Comment by Xuanting Cai Xuanting Cai 2011-04-26T19:36:09Z 2011-04-26T19:36:09Z Is this question too hard? I do not have any good idea yet. http://mathoverflow.net/questions/53314/why-must-a-reducible-flat-su2-connection-over-a-homology-sphere-be-trivial/53329#53329 Comment by Xuanting Cai Xuanting Cai 2011-04-18T16:07:17Z 2011-04-18T16:07:17Z $A^flat(M)/G(M)≅Hom(π_1(M),SU(2))/SU(2)$ is easy to prove. Just use geometric definition of connection. http://mathoverflow.net/questions/54496/what-is-the-definition-of-algebro-gemetric-quotient/54512#54512 Comment by Xuanting Cai Xuanting Cai 2011-02-06T21:54:02Z 2011-02-06T21:54:02Z I will check it. Thank you. http://mathoverflow.net/questions/54496/what-is-the-definition-of-algebro-gemetric-quotient/54512#54512 Comment by Xuanting Cai Xuanting Cai 2011-02-06T18:30:01Z 2011-02-06T18:30:01Z what I am really interested is following: I have a group G, finitely presented. Consider R(G)=HOM(G,SL(2,C)), the space of all reps of G into SL(2,C). Then SL(2,C) acts on R(G) naturally, i.e. conjugation. So the usual quotient of this action is the space of orbits, which are all conjugacy classes of reps. Now the algebro-geometric quotient is not this. It is the character variety of G. Thanks. http://mathoverflow.net/questions/53514/seiberg-witten-equation-on-s2-times-s1/53519#53519 Comment by Xuanting Cai Xuanting Cai 2011-01-27T23:19:44Z 2011-01-27T23:19:44Z OK. Thanks. So it is not a topological invariant? http://mathoverflow.net/questions/53314/why-must-a-reducible-flat-su2-connection-over-a-homology-sphere-be-trivial Comment by Xuanting Cai Xuanting Cai 2011-01-26T23:29:47Z 2011-01-26T23:29:47Z Of Course. Thank you for your help. http://mathoverflow.net/questions/53314/why-must-a-reducible-flat-su2-connection-over-a-homology-sphere-be-trivial/53356#53356 Comment by Xuanting Cai Xuanting Cai 2011-01-26T23:28:15Z 2011-01-26T23:28:15Z I am a knot theory student. Try to learn some 4 manifold thing. So maybe this is a dummy question for expert. Thank you. http://mathoverflow.net/questions/53314/why-must-a-reducible-flat-su2-connection-over-a-homology-sphere-be-trivial/53356#53356 Comment by Xuanting Cai Xuanting Cai 2011-01-26T23:06:12Z 2011-01-26T23:06:12Z Thanks for your explaination.