Extremal projections for contragredient Lie algebras and superalgebras of finite growth
Extremal projections for contragredient Lie algebras and superalgebras of finite growth
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矛盾李代数和有限增长超代数的极值投影
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发表时间：
1989
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通讯作者：
V N Tolstoi
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作者：
V N Tolstoi
1.有限维可逆李(超)-代数([11，[2])的极值投影为解决这些代数表示理论中的许多问题(约化或跨向量代数的刻划、不可约模的分类、模的子模分解)提供了一种强有力的通用方法。用于表示的基的构造、不同基之间互联系数装置的发展、动力学方程的对称性的研究，等等)。极值投影在无限维李(超)代数理论中起着同样重要的作用。本文给出了有限增长的无限维逆(超)李(超)代数(iCae-Moody(Super)jlgebtjSi.本文的结果对所有有限维或无限维逆梯度李(超)代数具有对称化的Cartan矩阵具有普适性。2.设g是任意有限增长的(有限维或无限维)逆李(超)代数，具有t>；可对称化的Cartan矩阵[3]，h是g的Cartan子代数，ΓΙ-{aj，a2，.。.，a r}iH-：g中的单根系，Δ+关于Π的正根系。以下是
1. The extremal projections of finite-dimensional contragredient Lie (super)-algebras ([11, [2]) provide a powerful and universal method for the solution of many problems in the representation theory of these algebras (the description of reduced or transvectorial algebras, the classification of irreducible modules, the decomposition of modules into submodules. the construction of bases for representations, the development of the apparatus of coefficients of interconnection between different bases, the study of symmetries of dynamical equations, and so on). Extremal projections play an equally Important role in the theory of infinite-dimensional Lie (super)algebxas. (n the present paper we give an explicit description of the extremal projections of infinite- dimensional contragredient Lie (super)algebras of finite growth (iCae-Moody (super)jlgebtjSi. The results here are universal for all contragradient Lie (super)algebvas of finite growth—finite- or infinite- dimensionul— possessing a symmetrizable Cartan matrix. 2. Let g be any (finite- or infinite-dimensional) contragredient Lie (super)algebru of finite growth possessing t> symmetrizable Cartan matrix [3], h the Cartan subalgebra of g, ΓΙ — {aj, a 2 , . . ., a r } ih-: system of simple radicals in g, and Δ + the system of positive radicals with respect to Π. following