Experimental Mathematics ( IF 0.5 ) Pub Date : 2019-11-18 , DOI: 10.1080/10586458.2019.1683102 Sofiane Bouarroudj 1 , Dimitry Leites 1 , Jin Shang 1
Abstract
A Lie (super)algebra with a nondegenerate invariant symmetric bilinear form B is called a nis-(super)algebra. The double extension of a nis-(super)algebra is the result of simultaneous adding to a central element and a derivation so that is a nis-algebra. Loop algebras with values in simple complex Lie algebras are most known among the Lie (super)algebras suitable to be doubly extended. In characteristic 2, the notion of double extension acquires specific features. Restricted Lie (super)algebras are among the most interesting modular Lie superalgebras. In characteristic 2, using Grozman’s Mathematica-based package SuperLie, we list double extensions of restricted Lie superalgebras preserving the nondegenerate closed 2-forms with constant coefficients. The results are proved for the number of indeterminates ranging from 4 to 7—sufficient to conjecture the pattern for larger numbers. Considering multigradings allowed us to accelerate computations up to 100 times.
中文翻译:
限制李超代数的双重扩展的计算机辅助研究保留非退化闭合 2-形式的特征 2
摘要
具有非退化不变对称双线性形式B的李(超)代数称为 nis-(超)代数。双重扩展nis-(超)代数的是同时添加到的结果一个中心元素和一个推导,使得是一个 nis 代数。具有简单复李代数中的值的环代数在适合双重扩展的李(超)代数中最为人所知。在特征 2 中,双重扩展的概念获得了特定的特征。受限李(超)代数是最有趣的模李超代数之一。在特征 2 中,使用 Grozman 的基于 Mathematica 的包 SuperLie,我们列出了限制李超代数的双重扩展,保留了具有常数系数的非退化闭 2-形式。结果证明了从 4 到 7 的不定数,足以推测更大数的模式。考虑到多重分级,我们可以将计算速度提高 100 倍。