現代数学の系譜工学物理雑談古典ガロア理論も読む78

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む78 (1002ﾚｽ)
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309: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/10/29(火) 15:53:35.79 ID:wEoW+rwB

>>305 訂正補足

失礼しました
”PSL(2,16):2 of degree 17”に相当するのは、
下記の 17T7 ”L(17):2=<PZL(2,16)”の方ですね（＾＾；
（PSL(2,16)の２倍の群。”=<”とは？ どういうつもりかな？ ）

で
17T7の方は、#fields＝0
17T6の方は、#fields＝3
ですね。詳しくは、下記のURLをどうぞ（＾＾

http://galoisdb.math.upb.de/groups?deg=17
http://galoisdb.math.upb.de/home A Database for Number Fields
Technische Universitat Kaiserslautern
http://galoisdb.math.upb.de/groups?deg=17
Transitive Groups of degree 17
(抜粋)
G　Name　|G|　|G| fact.　|Z(G)|　Properties of G　#fields
17T6　L(17)=PSL(2,16)　4080 24 ・ 3 ・ 5 ・ 17　1 not solvable, primitive, simple, irreducible, even 3
17T7　L(17):2=<PZL(2,16)　8160　25 ・ 3 ・ 5 ・ 17　1　not solvable, primitive, irreducible, even 0

http://galoisdb.math.upb.de/groups/view?deg=17&num=7
Transitive Group 17T7

http://www.lmfdb.org/GaloisGroup/17T7
LMFDB
Galois Group: 17T7

http://galoisdb.math.upb.de/groups/view?deg=17&num=6
Transitive Group 17T6

http://www.lmfdb.org/GaloisGroup/17T6
LMFDB
Galois Group: 17T6

http://rio2016.5ch.net/test/read.cgi/math/1571400076/309

579: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/11/07(木) 21:56:00.79 ID:+oKqujhC

>>577
>頂点作用素代数の構成

＜補足＞
”namely those of vertex algebras and Borcherds-Kac-Moody algebras, together with techniques of string theory, and applied them to the "moonshine module"”
ということです
常識だけどな

https://en.wikipedia.org/wiki/Richard_Borcherds
Richard Borcherds

Borcherds is best known for his resolution of the Conway-Norton monstrous moonshine conjecture, which describes an intricate relation between the monster group and modular functions on the complex upper half-plane.
To prove this conjecture, he drew upon theories that he had previously introduced, namely those of vertex algebras and Borcherds-Kac-Moody algebras,
together with techniques of string theory,
and applied them to the "moonshine module", a vertex operator algebra with monster symmetry constructed by Igor Frenkel, James Lepowsky, and Arne Meurman.
Additional work in moonshine concerned mod p variants of this conjecture, and were known as modular moonshine.

Later contributions include the theory of Borcherds products, which are holomorphic automorphic forms on O(n,2) that have well-behaved infinite product expansions at cusps.
Borcherds used this theory to resolve some long-standing conjectures concerning quasi-affineness of certain moduli spaces of algebraic surfaces.
More recently, Borcherds has rendered perturbative renormalization, in particular the 't Hooft-Veltman proof of perturbative renormalizability of gauge theory, into rigorous mathematical language.

http://rio2016.5ch.net/test/read.cgi/math/1571400076/579

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