Piecewise principal comodule algebras
By P. M. Hajac, U. Kraehmer, R. Matthes, Bartosz Zielinski. 2007
51 citations recorded by the source corpus.
A comodule algebra P over a Hopf algebra H with bijective antipode is called principal if the coaction of H is Galois and P is H-equivariantly projective (faithfully flat) over the coaction-invariant subalgebra B. We prove that principality is a piecewise property: given N comodule-algebra surjections P->Pi whose kernels intersect to zero, P is principal if and only if all Pi's are principal. Furthermore, assuming the principality of P, we show that the lattice these kernels generate is distributive if and only if so is the lattice obtained by intersection with B. Finally, assuming the above distributivity property, we obtain a flabby sheaf of principal comodule algebras over a certain space that is universal for all such N-families of surjections P->Pi and such that the comodule algebra of global sections is P.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f6fc236f905f7aa54817100d3f44666ad9ca0a23
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Topics in Noncommutative Geometry (2015, background): “It is worth mentioning principal comodule algebras, that are Hopf-Galois extensions satisfying an additional condition called “equivariant projectivity” [41], and principal extensions, that are principal comodule algebras satisfying two additional conditions [15].”
- Free actions of compact quantum group on unital C*-algebras (2013, background): “59, AH61]. In the same spirit, our main theorem (Theorem 0.4) unifies the C∗-algebraic concept of free actions of compact quantum groups [E-DA00] with the Hopf-algebraic concept of principal coactions [HKMZ11]. Theorem 0.4 implies the existence of strong connections [H-PM96] for free actions of compa”