Rigidity of quantum tori and the Andruskiewitsch–Dumas conjecture
Rigidity of quantum tori and the Andruskiewitsch–Dumas conjecture
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DOI：
10.1007/s00029-013-0145-3
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发表时间：
2012-04
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影响因子：
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通讯作者：
M. Yakimov
中科院分区：
文献类型：
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作者：
M. Yakimov
我们证明了安德鲁斯凯维奇-杜马猜想，任意有限维简单李代数的量化通用包络代数的正部的自同构群同构于 Dynkin 图 的自同构群和秩等于 的环面的半直积。我们证明的关键步骤是量子环面的刚性定理。它具有广泛的应用范围。它允许人们控制大类关联代数的（完全）自同构群，例如量子簇代数。
We prove the Andruskiewitsch–Dumas conjecture that the automorphism group of the positive part of the quantized universal enveloping algebraof an arbitrary finite dimensional simple Lie algebrais isomorphic to the semidirect product of the automorphism group of the Dynkin diagram ofand a torus of rank equal to the rank of. The key step in our proof is a rigidity theorem for quantum tori. It has a broad range of applications. It allows one to control the (full) automorphism groups of large classes of associative algebras, for instance quantum cluster algebras.