论文标题
部分可观测时空混沌系统的无模型预测
Sofic Lie Algebras
论文作者
论文摘要
我们介绍并研究了lie代数的soficity，以联想代数的线性soficity建立模型。我们介绍了同等的soficity定义，一个涉及度量超强，另一种涉及几乎表示。我们证明，次数生长的任何谎言代数都是sofic。我们还证明，在特征0的领域上的谎言代数是Sofic的，并且仅当其通用包膜代数是线性的SOFIC时。最后，我们为Witt和Virasoro代数提供了几乎代表的明确家庭。
We introduce and study soficity for Lie algebras, modelled after linear soficity in associative algebras. We introduce equivalent definitions of soficity, one involving metric ultraproducts and the other involving almost representations. We prove that any Lie algebra of subexponential growth is sofic. We also prove that a Lie algebra over a field of characteristic 0 is sofic if and only if its universal enveloping algebra is linearly sofic. Finally, we give explicit families of almost representations for the Witt and Virasoro algebras.
