We study the induction and restriction functor from a Hopf subalgebra of a semisimple Hopf algebra. The image of the induction functor is described when the Hopf subalgebra is normal. In this situation, at the level of characters this image is isomorphic to the image of the restriction functor. A criterion for subcoalgebras to be invariant under the adjoint action is given generalizing Masuoka’...

we show that every semi-artinian module which is contained in a direct sum of finitely presented modules in $si[m]$, is weakly co-semisimple if and only if it is regular in $si[m]$. as a consequence, we observe that every semi-artinian ring is regular in the sense of von neumann if and only if its simple modules are $fp$-injective.

This paper is a contribution to the construction of non-semisimple modular categories. We establish when M\"uger centralizers inside categories are also modular. As consequence, we obtain conditions under which relative monoidal centers give (non-semisimple) categories, and show that examples include representation small quantum groups. further derive representations more general groups, braide...

Let H be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If H is not semisimple and dim(H) = 2n for some odd integers n, then H or H * is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd primes p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p. In recent years, there has been some pro...

In this work, we attempt to investigate the connection between various types of ideals (for examples (m,n)-ideal, bi-ideal, interior-ideal, quasi-ideal, prime-ideal and maximal-ideal) of an ordered semigroup (S, ·,≤) and the corresponding, hyperideals of its EL-hyperstructure (S, ∗) (if exists). Moreover, we construct the class of EL-Γ-semihypergroup, associated to a partially-ordered Γsemigroup.

One from classical constructions of algebraic binary hyperstructures (semihypergroups and hypergroups) from ordered algebraic systems is based on a certain Lemma on principal ends generated by products of pairs of elements – shortly termed as Ends-Lemma. First version of this auxiliary lemma was obtained in the monography [3]. The mentioned lemma is applied not only in case of hyperstructures c...

We prove a Weyl Harish-Chandra integration formula for the action of a reductive dual pair on the corresponding symplectic space W. As an intermediate step, we introduce a notion of a Cartan subspace and a notion of an almost semisimple element in the symplectic space W. We prove that the almost semisimple elements are dense in W. Finally, we provide estimates for the orbital integrals associat...

We recall a version of the Osofsky-Smith theorem in the context of a Grothendieck category and derive several consequences of this result. For example, it is deduced that every locally finitely generated Grothendieck category with a family of completely injective finitely generated generators is semisimple. We also discuss the torsion-theoretic version of the classical Osofsky theorem which cha...

One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras. We prove that every contracted QUEA in a certain class is a cochain twist of the corresponding undeformed universal envelope. Consequently, these contracted QUEAs possess a triangular quasi-Hopf algebra structure. As examples, we consider κ-Poincar...