Hopf algebra constructions and representation theoryyvind SolbergØ. Solberg, “Hopf algebra constructions and representation theory,” Commun. Algebra, 17 , No. 7, 1775–1786 (1889).
A second construction for the deformation of the one-dimensional N-extended supersymmetric quantum mechanics is presented in the superspace representation, where the supersymmetry generators are realized in terms of operators belonging to the universal enveloping superalgebra of one bosonic and several ...
We begin in section 2 by considering the Kac-Palyutkin algebra, which occurs as H8 (n=2) in the Pansera construction, as well as B8 (m=2) in one of the Masuoka constructions. The Pansera construction is a generalization of the Kac-Palyutkin Hopf algebra and is an extension of the ...
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...
The Hopf moment map m gives immediately the representation of H on V . On the other hand, the anomalous Hopf symmetry exists only on the level of the algebra of observables and cannot be implemented on the space of states. 4 Scaling the harmonic oscillator Consider the anihilation and ...
We show that the gapped boundary is algebraically determined by a comodule algebra, or equivalently, a module algebra; and the gapped domain wall is determined by the bicomodule algebra, or equivalently, a bimodule algebra. The microscopic lattice constructions of the gapped boundary and domain ...
For any etale Lie groupoid G over a manifold M, the groupoid algebra C_c(G) of smooth functions with compact support on G has a natural coalgebra structure over C_c(M) which makes it into a Hopf algebroid. Conversely, for any Hopf algebroid A over C_c(M) we construct the ...
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...
Journal of Pure and Applied Algebra Universal constructions for Hopf algebrasPorst, Hanse