Symmetric self-adjoint Hopf categories and a categorical Heisenberg double
Symmetric self-adjoint Hopf categories and a categorical Heisenberg double
复制标题
对称自伴 Hopf 范畴和分类海森堡双范畴
DOI：
10.1093/qmath/haw050
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Elena Gal
中科院分区：
文献类型：
--
作者：
A. Gal;Elena Gal
受A. Zelevinsky关于正自伴Hopf代数的研究中，我们定义了一种我们称之为对称的自伴Hopf结构的半单交换范畴。已知每一个正的自伴Hopf代数都有一个相应的Heisenberg double的自然作用。我们构造规范态射提升的关系，定义这个行动的代数水平，并定义一个对象，我们称之为一个明确的海森堡双，这是一个自然的设置考虑这些态射。作为例子，我们给出了多项式函子和等变多项式函子范畴上的对称自伴Hopf结构.在多项式函子范畴的情况下，我们得到了无限维海森堡代数的Fock空间表示的范畴化。
Motivated by the work of of A. Zelevinsky on positive self-adjoint Hopf algebras, we define what we call a symmetric self-adjoint Hopf structure for a certain kind of semisimple abelian categories. It is known that every positive self-adjoint Hopf algebra admits a natural action of the associated Heisenberg double. We construct canonical morphisms lifting the relations that define this action on the algebra level and define an object that we call a categorical Heisenberg double that is a natural setting for considering these morphisms. As examples, we exhibit the symmetric self-adjoint Hopf structure on the categories of polynomial functors and equivariant polynomial functors. In the case of the category of polynomial functors we obtain categorification of the Fock space representation of the infinite-dimensional Heisenberg algebra.