相关论文: Construct Weak Hopf Algebras By Using Borcherds Ma…

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…

Let $B$ and $C$ be non-degenerate idempotent algebras and assume that $E$ is a regular separability idempotent in $M(B\otimes C)$. Define $A=C\otimes B$ and $\Delta:A\to M(A\otimes A)$ by $\Delta(c\otimes b)=c\otimes E\otimes b$. The pair…

In this paper we present the general theory of cleft extensions for a cocommutative weak Hopf algebra $H$. For a weak left $H$-module algebra we obtain a bijective correspondence between the isomorphisms classes of $H$-cleft extensions…

The Hopf envelope of a bialgebra is the free Hopf algebra generated by the given bialgebra. Its existence, as well as that of the cofree Hopf algebra, is a well-known fact in Hopf algebra theory, but their construction is not particularly…

In this paper we construct and study the representation theory of a Hopf C^*-algebra with approximate unit, which constitutes quantum analogue of a compact group C^*-algebra. The construction is done by first introducing a…

Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such that A is a Hopf subalgebra of E, H is a subcoalgebra in E…

We establish an embedding of the quantum enveloping algebra of a symmetric generalized Kac--Moody algebra into a localized Hall algebra of $\mathbb Z_2$-graded complexes of representations of a quiver with (possible) loops. To overcome…

By computing Frobenius-Schur indicators of modules of certain weak Hopf algebras, we give a formula for the number of involutions in symmetric groups, which are contained in a given coset with respect to a given Young subgroup.

We study a finite index inclusion of simple unital C*-algebras and construct a canonical completely positive coproduct on the second relative commutant, thereby endowing it with a natural coalgebra structure. Motivated by this construction,…

A. L. Agore and G. Militaru constructed a new invariant (a ``universal coacting Hopf algebra") for some finite-dimensional binary quadratic algebras such as Lie/Leibniz algebras, associative algebras, and Poisson algebras with prominent…

Multiplier Hopf algebroids are algebraic versions of quantum groupoids that generalize Hopf algebroids to the non-unital case and weak (multiplier) Hopf algebras to non-separable base algebras. The main structure maps of a multiplier Hopf…

Certain types of generalized undeformed and deformed boson algebras which admit a Hopf algebra structure are introduced, together with their Fock-type representations and their corresponding $R$-matrices. It is also shown that a class of…

We quantize the generalized-Witt algebra in characteristic 0 with its Lie bialgebra structures discovered by Song-Su (\cite{GY}). Via a modulo p reduction and a modulo "p-restrictedness" reduction process, we get 2^n{-}1 families of…

The elements of the wide class of quantum universal enveloping algebras are prooved to be Hopf algebras $H$ with spectrum $Q(H)$ in the category of groups. Such quantum algebras are quantum groups for simply connected solvable Lie groups…

We define some new algebraic structures, termed coloured Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set $\cal H$, corresponding to some parameter set $\cal Q$, with the transformations of…

In this paper, we introduce and study the notion of cointegrals in a weak multiplier Hopf algebras $(A, \Delta)$. A cointegral is a non-zero element $h$ in the multiplier algebra $M(A)$ such that $ah=\v_t(a)h$ for any $a\in A$. When $A$ has…

This article develops the theory of fusion categories acting on algebras. We will demonstrate that weak Hopf algebra actions on algebras correspond to specific actions of fusion categories. As an application of this theory, we introduce a…

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…

For a Poisson algebra $A$, by exploring its relation with Lie-Rinehart algebras, we prove a Poincar\'e-Birkoff-Witt theorem for its universal enveloping algebra $A^e$. Some general properties of the universal enveloping algebras of Poisson…

Let H be a cosemisimple Hopf algebra over an algebraically closed field k which contains a simple subcoalgebra of dimension 9. We show that if H has no simple subcoalgebras of even dimension then H contains either a grouplike element with…