Non-commutative connections of the second kind

2008/02/04 by Tomasz Brzeziński, Brzezinski, Tomasz · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0802.0445

openalex publication_date 2008/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A connection-like objects, termed \em hom-connections are defined in the realm of non-commutative geometry. The definition is based on the use of homomorphisms rather than tensor products. It is shown that hom-connections arise naturally from (strong) connections in non-commutative principal bundles. The induction procedure of hom-connections via a map of differential graded algebras or a differentiable bimodule is described. The curvature for a hom-connection is defined, and it is shown that flat hom-connections give rise to a chain complex.

Citations

• Flat connections and (co)modules

Cited by

• Smooth geometry of graded skew Clifford algebras
• A view toward the smooth geometry of Sklyanin algebras
• On differential smoothness of certain Artin-Schelter regular algebras of dimension 5

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