arXiv subjects

Waldeck Schützer

Publications and source records attributed to Waldeck Schützer.

4 recordsLinked to original sources

arXiv2024

Group gradings on triangularizable algebras

Classifying isomorphism classes of group gradings on algebras presents a compelling challenge, particularly within the realms of non-simple and infinite-dimensional algebras, which have been relatively unexplored. This study focuses on a kind of algebra that is neither simple nor finite-dimensional, aiming to classify the group gradings on triangularizable algebras as defined by Mesyan in 2019. The topology of infinite-dimensional algebras, along with the role of idempotent elements, plays a crucial role in our findings, leading to new insights and a deeper understanding of their structure.

math.RA↗

arXiv2022

On some H-cleft extensions which are distinguished by their polynomial H-identities

Let H be the Taft algebra over a finite commutative ring R. When N is a unit in R, we show that all H-cleft extensions over R are determined up to H-comodule algebra isomorphism by their polynomial H-identities.

math.RA↗

arXiv2022

On some H-Galois objects which are distinguished by their polynomial H-identities

When k is an algebraically closed field of characteristic 0 and H is a non-semisimple monomial Hopf algebra, we show that all Galois objects over H are determined up to H-comodule algebra isomorphism by their polynomial H-identities, extending a previous result by Kassel.

math.RA↗

arXiv2020

Gradings on Incidence Algebras and their Graded Polynomial Identities

Let P a locally finite partially ordered set, F a field, G a group, and I(P,F) the incidence algebra of P over F. We describe all the inequivalent elementary G-gradings on this algebra. If P is bounded, F is a infinite field of characteristic zero, and A, B are both elementary G-graded incidence algebras satisfying the same G-graded polynomial identities, and the automorphisms group of P acts transitively on the maximal chains of P , we show that A and B are graded isomorphic.

math.RA↗