In the work of Rostami et al., Bogomolov multiplier a Lie algebra L over field Ω is defined as particular factor subalgebra exterior product L∧L. If finite dimensional, we identify this object certain subgroup second cohomology group H2(L,Ω) by deriving Hopf-Type formula. As an application, affirmatively answer two questions posed Kunyavskiĭ regarding invariance under isoclinism algebras and ex...

The aim of this paper is to extend the classical Larson-Sweedler theorem, namely that a k-bialgebra has non-singular integral (and in particular Frobenius) if and only it finite dimensional Hopf algebra, ‘many-object’ setting categories. To end, we provide new characterizations Frobenius V-categories develop theory for V-categories. Our results apply algebras any braided monoidal category as sp...

Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra‎. ‎In this paper‎, ‎we investigate Gorenstein global dimensions for Hopf‎ ‎algebras and twisted smash product algebras $Astar H$‎. ‎Results from‎ ‎the literature are generalized‎. 

Inspired by [3] we introduce the concept of extended Hopf algebra and consider their cyclic cohomology in the spirit of Connes-Moscovici [3, 4, 5]. Extended Hopf algebras are closely related, but different from, Hopf algebroids. Their definition is motivated by attempting to define cyclic cohomology of Hopf algebroids in general. Many of Hopf algebra like structures, including the Connes-Moscov...

Quantum groups have been studied intensively for the last two decades from various points of view. The underlying mathematical structure is that of an algebra with a coproduct. Compact quantum groups admit Haar measures. However, if we want to have a Haar measure also in the noncompact case, we are forced to work with algebras without identity, and the notion of a coproduct has to be adapted. T...

Consider the coradical filtration of the Hopf algebras of planar binary trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We show that the associated graded Hopf algebras are dual to the cocommutative Hopf algebras introduced in the late 1980’s by Grossman and Larson. These Hopf algebras are constructed from ordered trees and heap-ordered trees, respectively. We also sho...

We introduce a notion of Hopf-Lie-Rinehart algebra and show that the universal algebra of a Hopf-Lie-Rinehart algebra acquires an ordinary Hopf algebra structure. Subject classification: Primary 16W30, Secondary 16S32 17B35

We generalize the notion of the rank-generating function of a graded poset. Namely, by enumerating different chains in a poset, we can assign a quasi-symmetric function to the poset. This map is a Hopf algebra homomorphism between the reduced incidence Hopf algebra of posets and the Hopf algebra of quasi-symmetric functions. This work implies that the zeta polynomial of a poset may be viewed in...

Let τ be an invertible skew pairing on (B,H), where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category HYD and there exists a Hopf algebra isomorphism w : B∞H → B τH in C, where B∞H is a Hopf algebra with (co)algebra structure the smash (c...