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[過去ﾛｸﾞ] ガロア第一論文及びその関連の資料スレ (1002ﾚｽ)
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354: １３２人目の素数さん [] 2023/02/12(日) 09:50:37.91 ID:t5GdbcIg

>>349 関連
>"vertex" dual resonance theory Kac Moody algebra

Kac?Moody Lie algebra（下記）
”E. Date, M. Jimbo, M. Kashiwara, T. Miwa,(1983)
The vertex operator constructions were, quite unexpectedly, applied to the theory of soliton equations. This was based on the observation (see [DaJiKaMi])
The vertex operators were introduced in string theory around 1969, but the vertex operator construction entered string theory only at its revival in the mid 1980s. Thus, the representation theory of affine algebras became an important ingredient of string theory (see [GrScWi]).(1987)
The vertex operators turned out to be useful even in the theory of finite simple groups. Namely, a twist of the homogeneous vertex operator construction based on the Leech lattice produced the 196883-dimensional Griess algebra and its automorphism group, the famous finite simple Monster group (see Sporadic simple group) [FrLeMe].(1989)”
そうなんだ。Kac?Moody Lie algebraだったね

(参考)
https://encyclopediaofmath.org/wiki/Kac-Moody_algebra
15 November 2017
Kac-Moody algebra
A Kac-Moody algebra (also Kac?Moody Lie algebra) is defined as follows:
Let A=(aij)ni,j=1  be an (n×n)
-matrix satisfying conditions (see Cartan matrix)
aii=2;aij?0 aij=0 and aij∈Z for i≠j,⇒ aji=0.}(a1)
The associated Kac?Moody algebra g(A) is a Lie algebra over C on 3ngenerators ei, fi, hi
(called the Chevalley generators) and the following defining relations:
略

つづく

http://rio2016.5ch.net/test/read.cgi/math/1615510393/354

897: １３２人目の素数さん [] 2023/02/27(月) 23:44:35.91 ID:k+s6pKPe

>>896 追加

1. Construction and Examples of Multiplier Ideals
This preliminary lecture is devoted to the construction and first properties of multiplier ideals.
We start by discussing the algebraic and analytic incarnations of these ideals.
After giving the example of monomial ideals, we survey briefly some of the invariants of singularities that can be defined via multiplier ideals.

＜google訳 一部手直し＞
1. 乗法イデアルの構成と例
この予備講義は、乗法イデアルの構築と最初の特性に専念しています。
これらのイデアルの代数的および解析的な具体化について議論することから始めます。
monomial idealsの例を示した後、乗法イデアルを介して定義できる特異点の不変量のいくつかを簡単に調べます。

（monomial ideal）
https://en.wikipedia.org/wiki/Monomial_ideal
Monomial ideal
In abstract algebra, a monomial ideal is an ideal generated by monomials in a multivariate polynomial ring over a field.
A toric ideal is an ideal generated by differences of monomials (provided the ideal is a prime ideal). An affine or projective algebraic variety defined by a toric ideal or a homogeneous toric ideal is an affine or projective toric variety, possibly non-normal.

http://rio2016.5ch.net/test/read.cgi/math/1615510393/897

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