157 research outputs found
On synthetic interpretation of quantum principal bundles
Quantum principal bundles or principal comodule algebras are re-interpreted
as principal bundles within a framework of Synthetic Noncommutative
Differential Geometry. More specifically, the notion of a noncommutative
principal bundle within a braided monoidal category is introduced and it is
shown that a noncommutative principal bundle in the category opposite to the
category of vector spaces is the same as a faithfully flat Hopf-Galois
extension.Comment: 18 page
Hopf modules and the fundamental theorem for Hopf (co)quasigroups
The notion of a Hopf module over a Hopf (co)quasigroup is introduced and a
version of the fundamental theorem for Hopf (co)quasigroups is proven.Comment: 11 pages; missing (co)associativity in Definition 2.1 adde
Curved differential graded algebras and corings
A relationship between curved differential algebras and corings is
established and explored. In particular it is shown that the category of
semi-free curved differential graded algebras is equivalent to the category of
corings with surjective counits. Under this equivalence, comodules over a
coring correspond to integrable connections or quasi-cohesive curved modules,
while contramodules over a coring correspond to a specific class of curved
modules introduced and termed Z-divergences in here.Comment: 25 page
Circle actions on a quantum Seifert manifold
The quotients of a (non-orientable) quantum Seifert manifold by circle
actions are described. In this way quantum weighted real projective spaces that
include the quantum disc and the quantum real projective space as special cases
are obtained. Bounded irreducible representations of the coordinate algebras
and the K-groups of the algebras of continuous functions on quantum weighted
real projective spaces are presented.Comment: 9 page
Divergences on projective modules and non-commutative integrals
A method of constructing (finitely generated and projective) right module
structure on a finitely generated projective left module over an algebra is
presented. This leads to a construction of a first order differential calculus
on such a module which admits a hom-connection or a divergence. Properties of
integrals associated to this divergence are studied, in particular the formula
of integration by parts is derived. Specific examples include inner calculi on
a noncommutative algebra, the Berezin integral on the supercircle and integrals
on Hopf algebras.Comment: 13 pages; v2 construction of projective modules has been generalise
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