Hopf algebra constructions and representation theoryyvind SolbergØ. Solberg, “Hopf algebra constructions and representation theory,” Commun. Algebra, 17 , No. 7, 1775–1786 (1889).
Hohlweg and C. Lange's associahedra [17]). We skip these constructions to keep this version short, but the interested reader can find details in [6]. Part 1. The Cambrian Hopf algebra 1.1. Cambrian trees In this section, we recall the definition and properties of “Cambrian trees”, ...
We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential calculi and connections using universal categorical constructions to capture...
mathematics,includingalgebra,hmctional analysis,representationtheory. Actionsandcoactionson algebras arean importantpart ofthe theoryof (weak)Hopfalgebras.In contrasttoother Hopfalgebraic constructionssuchas the quasi—Hopfalgebrasandweak quasi-Hopfalgebras.weakHopfalgebrasare coassociative.Thisallowsonetodeftne...
Let A be a Hopf algebra. In this section, we give the detailed elementary direct construc- tion, using lazy cocycles, of the group H 2 L (A) and some further preliminary constructions. We first recall some classical notions. The set of convolution invertible linear maps ...
6. As mentioned, this operator describes 'excitations moving on the quantum sphere' and in the field of a magnetic monopole. There is symmetry under the action of the quantum universal enveloping algebra Uq (su(2)) – the Hopf algebra dual to the quantum group SUq (2) – that allows ...
We conclude with some open problems and a categorification of these constructions.doi:10.1007/s10468-010-9258-yNantel BergeronThomas LamHuilan LiAlgebras and Representation TheoryN. Bergeron, T. Lam and H. Li, Combinatorial Hopf algebras and towers of algebra-dimension, quan- tization and functor...
We extend the notion of supercharacter theory to this context, and define a corresponding algebraic object that generalizes the Schur rings of the group algebra of a finite group. We show the existence of Hopf-algebraic analogues for the most common supercharacter theory constructions, specifici...
This textbook provides an introduction to fundamental concepts of algebra at upper undergraduate to graduate level, covering the theory of rings, fields and modules, as well as the representation theory of finite groups. Throughout the book, the exposition relies on universal constructions, making ...
(α,β)}(α,β)εG) in the sense of Van Daele and Wang (Comm Algebra, 2008) over a family of weak smash product algebras {H~(*cop)#H(α,β)}_((α,β)εG), and we obtain that WYD(H) is isomorphic to the representation category of the quasitriangular weak T-coalgebra WD(...