相关论文: Depth two, normality and a trace ideal condition f…

In this paper we investigate the question of normality for special monomial ideals in a polynomial ring over a field. We first include some expository sections that give the basics on the integral closure of a ideal, the Rees algebra on an…

We show that the isomorphism class of a two-step solvable Lie poset subalgebra of a semisimple Lie algebra is determined by its dimension. We further establish that all such algebras are absolutely rigid.

For each nontrivial semisimple Hopf algebra $H$ of dimension sixteen over $\mathbb{C}$, the smallest dimension inner-faithful representation of $H$ acting on a quadratic AS regular algebra $A$ of dimension 2 or 3, homogeneously and…

In this paper we determine the precise extent to which the classical sl_2-theory of complex semisimple finite-dimensional Lie algebras due to Jacobson--Morozov and Kostant can be extended to positive characteristic. This builds on work of…

A finite group G is called admissible over a given field if there exists a central division algebra that contains a G-Galois field extension as a maximal subfield. We give a definition of embedding problems of division algebras that extends…

In this paper we study some generalization of the notion of a formal group over ring, which may be called a formal group over Hopf algebra (FGoHA). The first example of FGoHA was found under the study of cobordism's ring of some $H$-space…

In this paper, we introduce and investigate \emph{bisemialgebras}and\emph{\ Hopf semialgebras} over commutative semirings. We generalize to the semialgebraic context several results on bialgebras and Hopf algebras over rings including the…

The method of subquotients is developed and used to determine all finite dimensional rank 2 Nichols algebras of diagonal type over an arbitrary field of characteristic zero. Key Words: Hopf algebra, Nichols algebra

We introduce the notion of the depth of a finite group $G$, defined as the minimal length of an unrefinable chain of subgroups from $G$ to the trivial subgroup. In this paper we investigate the depth of (non-abelian) finite simple groups.…

In this article we address a question concerning nilpotent Frobenius actions on Rees algebras and associated graded rings. We prove a nilpotent analog of a theorem of Huneke for Cohen-Macaulay singularities. This is achieved by introducing…

We present several constraints on the absolute Galois groups G_F of fields F containing a primitive pth root of unity, using restrictions on the cohomology of index p normal subgroups from a previous paper by three of the authors. We first…

In this article, we define and explore the weak normalization of an affine semigroup. In particular, for a fixed prime integer, we provide a geometric description of the weak normalization of an affine semigroup with respect to that prime,…

We continue studying properties of semisimple Hopf algebras $H$ over algebraically closed fields of characteristic 0 resulting from their generalized character tables. We show that the generalized character table of $H$ reflect normal left…

We introduce the Frobenius-Schur indicator for categories with duality to give a category-theoretical understanding of various generalizations of the Frobenius-Schur theorem, including that for semisimple quasi-Hopf algebras, weak Hopf…

In his foundational study of $p$-adic Hodge theory, Faltings introduced the method of almost \'etale extensions to establish fundamental comparison results of various $p$-adic cohomology theories. Scholze introduced the tilting operations…

Motivated by the study of depth 2 Frobenius extensions we introduce a new notion of Hopf algebroid. It is a 2-sided bialgebroid with a bijective antipode which connects the two, left and right handed, structures. While all the interesting…

Let $H$ be a connected spherical subgroup of a semisimple algebraic group $G$. In this paper, we give a criterion for $H$-orbit closures in the flag variety of $G$ to have nice geometric and cohomological properties. Our main tool is the…

Following the theory of principal $\infty$-bundles of Niklaus-Schreiber-Steveson, we develop a homotopy categorification of Hopf algebras, which model quantum groups. We study their higher-representation theory in the setting of…

We introduce the notion of the Frobenius-Perron dimension of an integral $\Bbb Z_+$-ring and give some applications of this notion to classification of finite dimensional quasi-Hopf algebras with a unique nontrivial simple module, and of…

We find a self-dual noncommutative and noncocommutative Hopf algebra acting as a universal symmetry on the modules over inner Frobenius algebras of modular categories (as used in two dimensional boundary conformal field theory) similar to…