发表机构
Escuela de Matemáticas, Universidad Industrial de Santander; Departamento de Matemáticas, Universidad de los Andes（坎塔布拉大学数学学院; 安第斯大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究强\(G -\)分次拟霍普夫代数的拟霍普夫理想分类，通过证明其与\((N,K)\)对应来分类，特定类拟霍普夫理想对应关系有改进，应用于余中心阿贝尔扩张等。
AI 中文摘要
设\(H\)是一个强\(G -\)分次拟霍普夫代数，其中\(G\)是任意群。我们通过证明\(H\)的每个拟霍普夫理想\(I\)对应于一对\((N,K)\)来对其拟霍普夫理想进行分类，其中\(N\)是\(G\)的正规子群，\(K\)是\(H_N=\bigoplus_{n\in N}H_n\)的\(G/N -\)不变拟霍普夫理想，其在分次映射下的像包含\(\Bbbk[N]\)的增广理想。对于特定类别的拟霍普夫理想，如那些具有相关拟霍普夫收缩的理想，或其提升商是交叉积的理想，我们进一步改进了这种对应关系。应用包括具有无限分次、有限中性分量和非平凡重结合子的余中心阿贝尔扩张。
英文摘要
We classify the quasi-Hopf ideals of quasi-Hopf algebras faithfully graded by arbitrary groups. Each ideal determines a normal subgroup, recording which degrees are identified in the quotient, together with an invariant ideal in the corresponding neutral component. We refine this description using an ideal of the original neutral component and a retraction of a naturally associated intermediate quotient. We prove that this intermediate quotient splits as the tensor product of its neutral component with the group algebra of the normal subgroup. For fixed subgroup and neutral-component data, the possible ideals, whenever they exist, form a torsor described by equivariant homomorphisms into central group-like elements. Our results require neither finite dimensionality nor bijectivity of the antipode. We apply them to cocentral abelian extensions with possibly infinite grading, finite-dimensional neutral component, and nontrivial reassociator.
Commentsv1: 38 pages; comments welcome. v2: 42 pages; open questions resolved, new results, Sections 5-6 restructured
