论文标题
立方狄拉克操作员和奇怪的弗洛伊达尔 - 佛罗里达州颜色谎言代数
Cubic Dirac operators and the strange Freudenthal-de Vries formula for colour Lie algebras
论文作者
论文摘要
本文的目的是为颜色代数定义立方狄拉克操作员。我们提供了必要且充分的条件，可以从$ε$ - Quadratic color lie代数的$ε$ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - Quadratic lie代数的代数。这用于证明基本颜色代数的一个奇怪的弗洛伊达尔 - 弗里斯公式以及用于颜色的立方狄拉克操作员的parthasarathy公式。我们计算了该狄拉克运算符引起的共同体，类似于Huang和Pandžić证明的代数Vogan猜想。
The aim of this paper is to define cubic Dirac operators for colour Lie algebras. We give a necessary and sufficient condition to construct a colour Lie algebra from an $ε$-orthogonal representation of an $ε$-quadratic colour Lie algebra. This is used to prove a strange Freudenthal-de Vries formula for basic colour Lie algebras as well as a Parthasarathy formula for cubic Dirac operators of colour Lie algebras. We calculate the cohomology induced by this Dirac operator, analogously to the algebraic Vogan conjecture proved by Huang and Pandžić.
