Hopf Algebroids from Noncommutative Bundles
نویسندگان
چکیده
We present two classes of examples Hopf algebroids associated with non-commutative principal bundles. The first comes from deforming the bundle while leaving unchanged structure algebra. second is related to a quantum homogeneous space; this needs careful deformation algebra in order preserve compatibilities between operations.
منابع مشابه
Hopf Algebroids and quantum groupoids
We introduce the notion of Hopf algebroids, in which neither the total algebras nor the base algebras are required to be commutative. We give a class of Hopf algebroids associated to module algebras of the Drinfeld doubles of Hopf algebras when the Rmatrices act properly. When this construction is applied to quantum groups, we get examples of quantum groupoids, which are semi-classical limits o...
متن کاملCleft Extensions of Hopf Algebroids
The notions of a cleft extension and a cross product with a Hopf algebroid are introduced and studied. In particular it is shown that an extension (with a Hopf algebroid H = (HL,HR)) is cleft if and only if it is HR-Galois and has a normal basis property relative to the base ring L of HL. Cleft extensions are identified as crossed products with invertible cocycles. The relationship between the ...
متن کاملOn Cohomology of Hopf Algebroids
Inspired by [3] we introduce the concept of extended Hopf algebra and consider their cyclic cohomology in the spirit of Connes-Moscovici [3, 4, 5]. Extended Hopf algebras are closely related, but different from, Hopf algebroids. Their definition is motivated by attempting to define cyclic cohomology of Hopf algebroids in general. Many of Hopf algebra like structures, including the Connes-Moscov...
متن کاملAnchored Vector Bundles and Algebroids
Inspired by recent works of Zang Liu, Alan Weinstein and Ping Xu, we introduce the notions of CC algebroids and non asymmetric Courant algebroids and study these structures. It is shown that CC algebroids of rank greater than 3 are the same as Courant algebroids up to a constant factor, though the definition of CC algebroids is much simpler than that of Courant algebroids,requiring only 2 axiom...
متن کاملA Schneider Type Theorem for Hopf Algebroids
Comodule algebras of a Hopf algebroid H with a bijective antipode, i.e. algebra extensions B ⊆ A by H, are studied. Assuming that a lifted canonical map is a split epimorphism of modules of the (non-commutative) base algebra of H, relative injectivity of the H-comodule algebra A is related to the Galois property of the extension B ⊆ A and also to the equivalence of the category of relative Hopf...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Reviews in Mathematical Physics
سال: 2023
ISSN: ['1793-6659', '0129-055X']
DOI: https://doi.org/10.1142/s0129055x23500277