相关论文: Frobenius extensions and weak Hopf algebras

We construct a `weak' version EM^w(K) of Lack & Street's 2-category of monads in a 2-category K, by replacing their compatibility constraint of 1-cells with the units of monads by an additional condition on the 2-cells. A relation between…

Aguiar and Mahajan's bimonoids A in a duoidal category M are studied. Under certain assumptions on M, the Fundamental Theorem of Hopf Modules is shown to hold for A if and only if the unit of A determines an A-Galois extension. Our findings…

Let $(A,\Delta)$ be a regular weak multiplier Hopf algebra. Denote by $E$ the canonical idempotent of $(A,\Delta)$ and by $B$ the image of the source map. Recall that $B$ is a non-degenerate algebra, sitting nicely in the multiplier algebra…

We investigate when a skew polynomial extension T = R[x; {\sigma}, {\delta}] of a Hopf algebra R admits a Hopf algebra structure, substantially generalising a theorem of Panov. When this construction is applied iteratively in characteristic…

We use canonical Markov extensions (Hofbauer towers) to give an explicit construction of the natural extensions of various measure preserving endomorphisms, and present some applications to particular examples.

In braided tensor categories we show the Maschke's theorem and give the necessary and sufficient conditions for double cross biproducts and crossbiproducts and biproducts to be bialgebras. We obtain the factorization theorem for braided…

We give a rigorous proof that the (codimension one) Connes-Moscovici Hopf algebra H_CM is isomorphic to a bicrossproduct Hopf algebra linked to a group factorisation of the group of positively-oriented diffeomorphisms of the real line. We…

In this paper we study the theory of cleft extensions for a weak bialgebra H. Among other results, we determine when two unitary crossed products of an algebra A by H are equivalent and we prove that if H is a weak Hopf algebra, then the…

To a depth two extension A | B, we associate the dual bialgebroids S := \End {}_BA_B and T := (A \o_B A)^B over the centralizer R=C_A(B). In the set-up where R is a subalgebra of B, which is quite common, two nondegenerate pairings of S and…

In this paper, we continue the study of weak multiplier Hopf algebras. We recall the notions of the source and target maps $\varepsilon_s$ and $\varepsilon_t$, as well as of the source and target algebras. Then we investigate these objects…

We show how, under certain conditions, an adjoint pair of braided monoidal functors can be lifted to an adjoint pair between categories of Hopf algebras. This leads us to an abstract version of Michaelis' theorem, stating that given a Hopf…

In this paper we explore minimum odd and minimum even depth sub algebra pairs in the context of double cross products of finite dimensional Hopf algebras. We start by defining factorization algebras and outline how subring depth in this…

Let $\mathscr{M}$ be a $II_1$ factor acting on the Hilbert space $\mathscr{H}$, and $\mathscr{M}_{\textrm{aff}}$ be the Murray-von Neumann algebra of closed densely-defined operators affiliated with $\mathscr{M}$. Let $\tau$ denote the…

Given a II$_1$ factor $M$, a W$^*$-subalgebra $Q\subset M$ is {\it compressible} if for any $\varepsilon>0$ there exists a finite set of unitary elements $\Cal U_0\subset \Cal U(M)$ such that $\| \frac{1}{|\Cal U_0|}\sum_{u\in \Cal U_0}…

We consider finite-dimensional Hopf algebras $u$ which admit a smooth deformation $U\to u$ by a Noetherian Hopf algebra $U$ of finite global dimension. Examples of such Hopf algebras include small quantum groups over the complex numbers,…

We give a necessary and sufficient condition for two Hopf algebras presented as central extensions to be isomorphic, in a suitable setting. We then study the question of isomorphism between the Hopf algebras constructed in 0707.0070v1 as…

We present several applications of the weak specification property and certain topological Markov properties, recently introduced by S. Barbieri, F. Garc\'{i}a-Ramos and H. Li, and implied by the pseudo-orbit tracing property, for general…

We introduce a notion of depth three tower of three rings C < B < A as a useful generalization of depth two ring extension. If A = End B_C and B | C is a Frobenius extension, this also captures the notion of depth three for a Frobenius…

We introduce the Markov extension, represented schematically as a tower, to the study of dynamical systems with holes. For tower maps with small holes, we prove the existence of conditionally invariant probability measures which are…

Let $R_s M$ denote the Singer construction on an unstable module $M$ over the Steenrod algebra $A$ at the prime two; $R_s M$ is canonically a subobject of $P_s\otimes M$, where $P_s$ is the polynomial algebra on s generators of degree one.…