Timeline for How are $SU(n)$, $SL(n)$ and $\mathfrak{sl}(n,\mathbb{C})$ related?

7 events

when toggle format	what		by	license	comment
Jun 28, 2019 at 15:26	vote	accept	Andrius Kulikauskas
Jun 27, 2019 at 19:09	comment	added	Andrius Kulikauskas		Thank you, @Torsten-Schoeneberg , for your edit! I appreciate the extra information. I'm digesting this all.
Jun 27, 2019 at 16:51	history	edited	Torsten Schoeneberg	CC BY-SA 4.0	added paragraph about groups vs. algebras
Jun 26, 2019 at 23:02	history	edited	Torsten Schoeneberg	CC BY-SA 4.0	added 652 characters in body
Jun 26, 2019 at 19:11	comment	added	Torsten Schoeneberg		Yes, that's what I mean. Since I mostly work on the Lie algebra level, where the distinction is really whether the algebra is viewed as a vector space over $\mathbb R$ or $\mathbb C$, I often just use that terminology.
Jun 26, 2019 at 18:59	comment	added	Andrius Kulikauskas		Profoundly helpful, @Torsten-Schoeneberg , THANK YOU! I think this is the big picture answer, with many details, that I need in order to understand this subject. Tomorrow I will study further what you've written. One question: I appreciate the distinction between a real Lie group (with smooth maps on a real smooth manifold) and a complex Lie group (with holomorphic maps on a complex-analytic manifold). Is that what you mean by the base field being $\mathbb{R}$ or $\mathbb{C}$?
Jun 26, 2019 at 17:57	history	answered	Torsten Schoeneberg	CC BY-SA 4.0