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Dichte Ringe*

Günther Haugner, Wolfgang Zimmermann (1974)

Mathematische Annalen

Differential calculus on almost commutative algebras and applications to the quantum hyperplane

Cătălin Ciupală (2005)

Archivum Mathematicum

In this paper we introduce a new class of differential graded algebras named DG ρ -algebras and present Lie operations on this kind of algebras. We give two examples: the algebra of forms and the algebra of noncommutative differential forms of a  ρ -algebra. Then we introduce linear connections on a  ρ -bimodule M over a  ρ -algebra  A and extend these connections to the space of forms from A to M . We apply these notions to the quantum hyperplane.

Differential smoothness of affine Hopf algebras of Gelfand-Kirillov dimension two

Tomasz Brzeziński (2015)

Colloquium Mathematicae

Two-dimensional integrable differential calculi for classes of Ore extensions of the polynomial ring and the Laurent polynomial ring in one variable are constructed. Thus it is concluded that all affine pointed Hopf domains of Gelfand-Kirillov dimension two which are not polynomial identity rings are differentially smooth.

Differentiation and splitting for lattices over orders

Wolfgang Rump (2001)

Colloquium Mathematicae

We extend our module-theoretic approach to Zavadskiĭ’s differentiation techniques in representation theory. Let R be a complete discrete valuation domain with quotient field K, and Λ an R-order in a finite-dimensional K-algebra. For a hereditary monomorphism u: P ↪ I of Λ-lattices we have an equivalence of quotient categories ̃ u : Λ - l a t / [ ] δ u Λ - l a t / [ B ] which generalizes Zavadskiĭ’s algorithms for posets and tiled orders, and Simson’s reduction algorithm for vector space categories. In this article we replace u by a more...

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