Timeline for What sort of ring-theoretic properties does the representation ring of a compact Lie group possess?
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7 events
| when toggle format | what | by | license | comment | |
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| Feb 10, 2014 at 23:25 | vote | accept | David Roberts♦ | ||
| Feb 10, 2014 at 13:11 | comment | added | Jim Humphreys | @David: I should have added an online link to Segal's 1968 paper: numdam.org/numdam-bin/fitem?id=PMIHES_1968__34__113_0 (which Serre discusses in the finite group case, in his textbook on finite group representations). | |
| Feb 10, 2014 at 4:23 | comment | added | David Roberts♦ | In fact, I just found that Segal proved $R(G)$ is finitely generated for any compact $G$, by using finite generation over $R(U(n))$. | |
| Feb 10, 2014 at 0:56 | comment | added | Qiaochu Yuan | @Jim: thanks for the reference! My claim above is Proposition 2.1 in that section, and the more precise information when $G$ is simply connected is Corollary 2.11. In this case $R(G)$ is actually the polynomial ring on $r$ variables where $r$ is the rank. | |
| Feb 10, 2014 at 0:15 | comment | added | Jim Humphreys | Note that a good reference for the structure of representation rings is section VI.2 of Springer GTM 98 Representations of Compact Lie Groups by Brocker and tom Dieck. In particular, the ring is finitely generated (hence noetherian) and has more precise properties if $G$ is simply connected, etc. | |
| Feb 9, 2014 at 23:49 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
added 328 characters in body
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| Feb 9, 2014 at 23:44 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |