In this paper we introduce the concepts of hyper P -semisimple Ialgebra and Abelian hyper I-algebra and we state and prove some related results. The hyper p-semi simple I-algebras is a generalization of p-semisimple BCI-algebras and a subclass of hyper I-algebras. Specially we show that every Abelian hyper I-algebra is a hyper psemisimple I-algebra and a commutative canonical hypergroup. In fol...

Abstract For a semisimple Lie algebra defined over discrete valuation ring with field of fractions K , we prove that any primitive ideal rational central character in the affinoid enveloping algebra, $$\widehat{U({\mathfrak {g}})_{K}}$$ U ( g )</...

Let G be a connected reductive p-adic group and let g be its Lie algebra. LetO be a G-orbit in g. Then the orbital integral μO corresponding to O is an invariant distribution on g, and Harish-Chandra proved that its Fourier transform μ̂O is a locally constant function on the set g′ of regular semisimple elements of g. Furthermore, he showed that a normalized version of the Fourier transform is l...

Let p, q be distinct prime numbers, and k an algebraically closed field of characteristic 0. Under certain restrictions on p, q, we discuss the structure of semisimple Hopf algebras of dimension pq. As an application, we obtain the structure theorems for semisimple Hopf algebras of dimension 9q over k. As a byproduct, we also prove that odd-dimensional semisimple Hopf algebras of dimension less...

We extend two well-known results on primitive ideals in enveloping algebras of semisimple Lie algebras, the Irreducibility theorem and Duflo theorem, to much wider classes of algebras. Our general version of Irreducibility theorem says that if A is a positively filtered associative algebra such that grA is a commutative Poisson algebra with finitely many symplectic leaves, then the associated v...

We relate commutative algebras in braided tensor categories to braid-reversed equivalences, motivated by vertex algebra representation theory. First, for $\mathcal{C}$ a category, we give detailed construction of the canonical $\mathcal{C}\boxtimes\mathcal{C}^\text{rev}$: if is semisimple but not necessarily finite or rigid, then $\bigoplus_{X\in\text{Irr}(\mathcal{C})}X'\boxtimes X$ algebra, w...

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 preserving and order reflecting map between morphisms of the Weyl groupoid and graded right coideal subalgebras of the Nichols algebra. Here morphisms are orde...