Related papers: Homological Integrals for Weak Hopf Algebras

Let $H$ be an infinite-dimensional braided Hopf algebra and assume that the braiding is symmetric on $H$ and its quasi-dual $H^d$. We prove the Blattner-Montgomery duality theorem, namely we prove $$ (R # H)# H^{d} \cong R \otimes (H #…

We prove, for quasicompact separated schemes over ground fields, that Cech cohomology coincides with sheaf cohomology with respect to the Nisnevich topology. This is a partial generalization of Artin's result that for noetherian schemes…

We study algebraic and homological properties of two classes of infinite dimensional Hopf algebras over an algebraically closed field k of characteristic zero. The first class consists of those Hopf k-algebras that are connected graded as…

We prove the weak functoriality of (big) Cohen-Macaulay algebras, which controls the whole skein of "homological conjectures" in commutative algebra [H1][HH2]. Namely, for any local homomorphism $ R\to R'$ of complete local domains, there…

A finite-dimensional Hopf algebra is called quasi-split if it is Morita equivalent to a split abelian extension of Hopf algebras. Combining results of Schauenburg and Negron, it is shown that every quasi-split finite-dimensional Hopf…

We extend the notion of semi-infinite cohomology of Lie algebras to include cases where the Lie algebra does not admit a semi-infinite structure but satisfies a mild condition. Our construction clarifies the definition of affine W-algebras…

In this paper, we construct the weak version of peak quasisymmetric functions inside the Hopf algebra of weak composition quasisymmetric functions (WCQSym) defined by Guo, Thibon and Yu. Weak peak quasisymmetric functions (WPQSym) are…

We recall the notion of a Hopf (co)quasigroup defined in \cite{Kl09} and define integration and Fourier Transforms on these objects analogous to those in the theory of Hopf algebras. Using the general Hopf module theory for Hopf…

Comodule algebras of a Hopf algebroid H with a bijective antipode, i.e. algebra extensions B\subseteq A by H, are studied. Assuming that a lifted canonical map is a split epimorphism of modules of the non-commutative base algebra of H,…

We give a geometric proof of inverse Hamiltonian reduction for all affine W-algebras in type A at generic level, a certain embedding of the affine W-algebra corresponding to an arbitrary nilpotent in $\mathfrak{gl}_N$ into that…

We prove that, in case $A(c)$ = the FRT construction of a braided vector space $(V,c)$ admits a weakly Frobenius algebra $\mathfrak B$ (e.g. if the braiding is rigid and its Nichols algebra is finite dimensional), then the Hopf envelope of…

In this note, we show that every Noetherian graded ring with an affine degree zero part is affine. As a result, a Noetherian graded Hopf algebra whose degree zero component is a commutative or a cocommutative Hopf subalgebra is affine.…

We investigate the reflection theory of Nichols algebras over arbitrary coquasi-Hopf algebras with bijective antipode, generalizing previous results restricted to the pointed cosemisimple setting [47]. By establishing a braided monoidal…

We study graded right coideal subalgebras of Nichols algebras of semisimple Yetter-Drinfeld modules. Assuming that the Yetter-Drinfeld module admits all reflections and the Nichols algebra is decomposable, we construct an injective order…

In this paper, we establish the sheafified version of the cohomological integrality conjecture for stacks obtained as a quotient of a smooth affine symmetric algebraic variety by a reductive algebraic group equipped with an invariant…

In this paper we introduce the notion of weak operator and the theory of Yetter-Drinfeld modules over a weak braided Hopf algebra with invertible antipode in a strict monoidal category. We prove that the class of such objects constitutes a…

We extend Schaumann's theory of pivotal structures on fusion categories matched to a module category and of module traces developed in arXiv:1206.5716 to the case of non-semisimple tensor categories, and use it to study eigenvalues of the…

We investigate the splitting property of quasitriangular Hopf algebras through the lens of twisted tensor products. Specifically, we demonstrate that an infinite-dimensional quasitriangular Hopf algebra possesses the splitting property if…

We study universal enveloping Hopf algebras of Lie algebras in the category of weakly complete vector spaces over the real and complex field.

Let $B \subset A$ be a depth $2$ inclusion of simple unital $C^*$-algebras with a conditional expectation of index-finite type. We show that the second relative commutant $B' \cap A_1$ carries a canonical structure of a weak $C^*$-Hopf…