Quantum Tori and the Structure of Elliptic Quasi-simple Lie Algebras
Quantum Tori and the Structure of Elliptic Quasi-simple Lie Algebras
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DOI：
10.1006/jfan.1996.0013
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发表时间：
1996-02
影响因子：
1.7
通讯作者：
S. Berman;Yung Gao;Y. Krylyuk
中科院分区：
文献类型：
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作者：
S. Berman;Yung Gao;Y. Krylyuk
摘要 我们对那些简单系带且秩为l⩾3的驯化不可约椭圆拟单李代数进行了研究和分类。第一步是通过识别坐标来识别这种代数的核心直到中心同源性。当类型为DorE时，坐标是ν变量中的洛朗多项式，而对于类型A，坐标可以是ν变量中的任何量子环面。下一步是研究通用中心扩张以及核心的推导代数。这些与坐标的第一 Connes 循环同调群有关。最后一步是使用这些信息给出李代数的构造，然后我们证明它产生上述代数类型的所有同构类的代表。
Abstract We study and classify those tame irreducible elliptic quasi-simple Lie algebras which are simply laced and of rankl⩾3. The first step is to identify the core of such an algebra up to central isogeny by identifying the coordinates. When the type isDorEthe coordinates are Laurent polynomials in ν variables, while for typeAthe coordinates can be any quantum torus in ν variables. The next step is to study the universal central extension as well as the derivation algebra of the core. These are related to the first Connes cyclic homology group of the coordinates. The final step is to use this information to give constructions of Lie algebras which we then prove yield representatives of all isomorphism classes of the above types of algebras.