Extending abelian categories, and also the p-exact ones, these notions include the usualdomainsof homology and homotopy theories, e.g. the category of ‘pairs’ of topological spaces or groups; they also include theircodomains, since the sequences of homotopy ‘objects’ for a pair of pointed...
Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra, ln this paper, we characterize the projectivity (injectivity) of M as a left A#σ H-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σ H, ...
J. Browkin proved that G n(ℚ) is a subgroup of K 2ℚ if n = 1, 2, 3, 4 or 6 and conjectured that G n (ℚ) is not a group for any other values of n. This conjecture was confirmed for n = 2 r 3 s or n = p r , where p ≥ 5 is a prime number such ...
Exotic derived categories, contramodules, semialgebras, infinite-dimensional Lie algebras, algebraic Harish-Chandra pairs, and locally compact totally disconnected topological groups all interplay in the theories developed in this monograph Includes supplementary material: sn.pub/extras Part of the book seri...
In [W], it was used as a key part in topological and holomorphic twists of supersymmetric field theories. Twisting a supersymmetric field theory gives rise to simpler field theories that can be topological (giving a TQFT), holomorphic, or something in between, depending on properties of the ...
Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra, ln this paper, we characterize the projectivity (injectivity) of M as a left A#σ H-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σ H, ...
Journal of AlgebraI. Hofstetter, Extensions of Hopf Algebras and their Cohomological Description, J. Algebra 164 (1994), 264-298.Hofstetter, I.: Extensions of Hopf algebras and their cohomological description, J. Algebra 164 (1994), 264–298....
The left and right homological integrals are introduced for a large class of\ninfinite dimensional Hopf algebras. Using the homological integrals we prove a\nversion of Maschke's theorem for infinite dimensional Hopf algebras. The\ngeneralization of Maschke's theorem and homological integrals are the...
We generalize this result to the quantum shuffle product, associated to a class of non-commutative algebras (for example all the Hopf algebras). As a first application we show that the Hochschild–Serre identity is the dual statement of our result. In particular, we extend this identity to ...
The utilization of the methods of sheaf theory and sheaf cohomology to capture the essential aspects of gauge theories has been elaborated in detail by Mallios [24,25], inspired by the approach suggested initially by Selesnick [26]. We employ similar sheaf cohomological concepts targeting the ...