Compact groups as algebraic groups

نویسنده

  • Bill Casselman
چکیده

Aclassic result of [Tannaka:1939], in the formulation of [Chevalley:1946], asserts that every compact subgroup of GLn(C) is the group of real points on an algebraic group defined over R. Chevalley introduced a more algebraic approach to the topic, but his underlying argument is not so different from Tannaka’s. The literature since then has followed one of two threads. One is algebraic (as in Chapter 9 of [Robert:1983]), inspired by Grothendieck’s notion of Tannakian categories (as in [Grothendieck:1970]). The other is analytic (as in §XI.11 of [Yoshida:1965] or §30 of [Hewitt-Ross:1970]), and follows Tannaka’s original exposition more closely. There is surprisingly little overlap between the two, and in fact neither group seems to be very aware of the other. There is an account somewhere in between in [Bröcker-tom Dieck:1985], but nonetheless it looks to me as if there were room for clarification. In this essay I shall offer a brief argument that takes advantage of terminology and concepts that have been introduced since Chevalley’s book was written. The basic ideas are still due to Chevalley.

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تاریخ انتشار 2015