𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Duality for Hopf Algebroids

✍ Scribed by Dmitriy Rumynin

Book ID
102575291
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
138 KB
Volume
223
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Our goal is twofold. First, we formulate a duality between commutative bialgebroids and cocommutative bialgebras over a ring extension. Second, we show that for a certain action groupoid J, the Hopf algebroid of functions on the Frobenius kernel J 1 is dual to the restricted enveloping algebra of the Lie algebroid of J.

πŸ“œ SIMILAR VOLUMES

Tannaka-Krein duality for Hopf algebroid
Tannaka-Krein duality for Hopf algebroids
✍ PhΓΉng HΓ΄ Hai πŸ“‚ Article πŸ“… 2008 πŸ› The Hebrew University Magnes Press 🌐 English βš– 234 KB
Integral Theory for Hopf Algebroids
Integral Theory for Hopf Algebroids
✍ Gabriella BΓΆhm πŸ“‚ Article πŸ“… 2005 πŸ› Springer Netherlands 🌐 English βš– 373 KB
Cleft Extensions of Hopf Algebroids
Cleft Extensions of Hopf Algebroids
✍ Gabriella BΓΆhm; Tomasz BrzeziΕ„ski πŸ“‚ Article πŸ“… 2006 πŸ› Springer 🌐 English βš– 742 KB
Monoidal Bicategories and Hopf Algebroid
Monoidal Bicategories and Hopf Algebroids
✍ Brian Day; Ross Street πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 826 KB

Why are groupoids such special categories? The obvious answer is because all arrows have inverses. Yet this is precisely what is needed mathematically to model symmetry in nature. The relation between the groupoid and the physical object is expressed by an action. The presence of inverses means that

The cyclic theory of Hopf algebroids
The cyclic theory of Hopf algebroids
✍ Kowalzig, Niels; Posthuma, Hessel πŸ“‚ Article πŸ“… 2011 πŸ› European Mathematical Society 🌐 English βš– 489 KB