论文标题
新的简单谎言超级甲壳虫作为奇异的联想代数
New simple Lie superalgebras as queerified associative algebras
论文作者
论文摘要
超过$ \ mathbb {c} $，蒙哥马利超级化的赫斯坦（Herstein）从有限维二维的联想代数中建造了简单的lie代数，发现了该过程的障碍，并将其应用于$ \ mathbb {z}/2 $ 2 $ graded groladed cossopiative sossosiative sossiciative sossiative of dictionial coplyal coefferients。 自1990年代以来，Vasiliev和Konstein及其合着者（通过Herstein--Montgomery方法，重新发现了它）的简单谎言（超级）代数（超级）代数（例如Vasiliev的代数，例如Vasiliev的较高的自旋代数（又称symerver）模型，并构成了分析的模型。 “ Queerification”是另一种烹饪简单的超级级别的方法，来自简单的联想（超级）代数。可以通过添加类似于faddeev--popov ghosts的新元素来“ Queerized”的上面的联想（超级）代数（超级）代数和谎言（超级）代数（超级）代数。 猜想：1）“ Queerified” Hamiltonian描述了Calogero型号的版本，其中$ 1 \ vert 1 $维度时间； 2）谎言超级代数的代数和非均匀的亚代代代数自然扩大了未来理论的超对称性； 3）只有分级交换代数才能模仿合理丰富的非交通几何形状中功能的代数。
Over $\mathbb{C}$, Montgomery superized Herstein's construction of simple Lie algebras from finite-dimensional associative algebras, found obstructions to the procedure and applied it to $\mathbb{Z}/2$-graded associative algebra of differential operators with polynomial coefficients. Since the 1990s, Vasiliev and Konstein with their co-authors constructed (via the Herstein--Montgomery method, having rediscovered it) simple Lie (super)algebras from the associative (super)algebra such as Vasiliev's higher spin algebras (a.k.a. algebras of observables of the rational Calogero model) and algebras of symplectic reflections. The "queerification" is another method for cooking a~simple Lie superalgebra from the simple associative (super)algebra. The above examples of associative (super)algebras, and Lie (super)algebras of "matrices of complex size" can be "queerified" by adding new elements resembling Faddeev--Popov ghosts. Conjectures: 1) a "queerified" Hamiltonian describes a version of the Calogero model with $1\vert 1$-dimensional time; 2) metabelean algebras and inhomogeneous subalgebras of Lie superalgebras naturally widen supersymmetries in future theories; 3) only graded-commutative algebras can imitate algebras of functions in a reasonably rich non-commutative Geometry.
