论文标题
广义还原谎言代数的BGG类别
The BGG Category for Generalised Reductive Lie Algebras
论文作者
论文摘要
据说，如果它是半imple lie代数的直接总和，则据说是一个概括的还原性。在本文中，我们将BGG类别$ \ MATHCAL {O} $扩展到复杂的半imple lie代数到类别$ \ Mathcal {O'} $，而不是复杂的广义还原谎言代数。然后，我们对此新类别的最高权重模块和投影模块进行初步研究，并在经典情况下概括了一些结论。作为与复杂的半完整谎言代数案例的关键区别，我们证明$ \ Mathcal {o'} $中没有投影模块。
A Lie algebra is said to be generalised reductive if it is a direct sum of a semisimple Lie algebra and a commutative radical. In this paper we extend the BGG category $\mathcal{O}$ over complex semisimple Lie algebras to the category $\mathcal {O'}$ over complex generalised reductive Lie algebras. Then we make a preliminary research on the highest weight modules and the projective modules in this new category $\mathcal {O'}$, and generalize some conclusions in the classical case. As a critical difference from the complex semisimple Lie algebra case, we prove that there is no projective module in $\mathcal {O'}$.
