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- Dalhousie UniversityCA11 papers
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13 papers · 1 filter
Almost fine gradings on algebras and classification of gradings up to isomorphism
Alberto Elduque, Mikhail Kochetov
We consider the problem of classifying gradings by groups on a finite-dimensional algebra (with any number of multilinear operations) over an algebraically closed field. We int…
Graded-division algebras over arbitrary fields
Yuri Bahturin, Alberto Elduque, Mikhail Kochetov
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary grou…
Matrices over a commutative ring as sums of three idempotents or three involutions
Gaohua Tang, Yiqiang Zhou, Huadong Su
Motivated by Hirano-Tominaga's work \cite{HT} on rings for which every element is a sum of two idempotents and by de Seguins Pazzis's results \cite{de} on decomposing every matrix…
Simple Graded Division Algebras over the Field of Real Numbers
Yuri Bahturin, Mikhail Zaicev
We classify, up to equivalence, all finite-dimensional simple graded division algebras over the field of real numbers. The grading group is any finite abelian group.
Rings in which every element is either a sum or a difference of a nilpotent and an idempotent
Simion Breaz, Peter Danchev, Yiqiang Zhou
{Generalizing the notion of nil cleanness from \cite{D13}, in parallel to \cite{DM14}, we define the concept of {\it weak nil cleanness} for an arbitrary ring. Its comprehensive st…
On rigidity of Nichols algebras
Iván Angiono, Mikhail Kochetov, Mitja Mastnak
We study deformations of graded braided bialgebras using cohomological methods. In particular, we show that many examples of Nichols algebras, including the finite-dimensional ones…