[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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355(2): 2023/02/12(日)09:51 ID:t5GdbcIg(2/12) AAS
>>354
つづき

A systematic study of Kac-Moody algebras was started independently by V.G. Kac [Ka] and R.V. Moody [Mo], and subsequently many results of the theory of finite-dimensional semi-simple Lie algebras have been carried over to Kac-Moody algebras. The main technical tool of the theory is the generalized Casimir operator (cf. Casimir element), which can be constructed provided that the matrix A
is symmetrizable, i.e. A=DB
for some invertible diagonal matrix D
and symmetric matrix B
[Ka2]. In the non-symmetrizable case more sophisticated geometric methods are required [Ku], [Ma].
省5

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356(1): 2023/02/12(日)09:51 ID:t5GdbcIg(3/12) AAS
>>355
つづき

The basic representation of g(A(1))
is then defined on V
by the following formulas [FrKa]:

π(u(n))=u(n),u∈h
π(E(n)α)=Xn(α)cα,π(k)=1;
省6

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358: 2023/02/12(日)09:58 ID:d0d29vIc(3/6) AAS
>>354-357
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