8 papers
A linear algebra approach to graded Frobenius algebras
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu +1
If is a finite-dimensional algebra graded by a group , and , we define a variant of paratrophic matrix associated with and , and we use it to characterize the…
Graded Frobenius algebras from tensor algebras of bimodules
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
We consider certain quotient algebras of tensor algebras of bimodules over a finite-dimensional algebra , and we investigate Frobenius type properties of such algebras. Our…
Picard groups of quasi-Frobenius algebras and a question on Frobenius strongly graded algebras
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
Our initial aim was to answer the question: does the Frobenius (symmetric) property transfers from a strongly graded algebra to its homogeneous component of trivial degree? Related…
Graded Frobenius Rings
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter…
Bicrossed products with the Taft algebra
A. L. Agore, L. Nastasescu
Let be a group which admits a generating set consisting of finite order elements. We prove that any Hopf algebra which factorizes through the Taft algebra and the group Hopf al…
Symmetric algebras of corepresentations and smash products
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
We investigate Frobenius algebras and symmetric algebras in the monoidal category of right comodules over a Hopf algebra ; for the symmetric property is assumed to be cosove…
Graded semisimple algebras are symmetric
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
We study graded symmetric algebras, which are the symmetric monoids in the monoidal category of vector spaces graded by a group. We show that a finite dimensional graded semisimple…
Frobenius algebras of corepresentations: gradings
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
We consider Frobenius algebras in the monoidal category of right comodules over a Hopf algebra . If is a group Hopf algebra, we study a more general Frobenius type property…