Results 21 to 30 of about 4,745 (95)
Pointed Hopf algebras over nonabelian groups with nonsimple standard braidings
Proceedings of the London Mathematical Society, Volume 127, Issue 4, Page 1185-1245, October 2023., 2023 Abstract We construct finite‐dimensional Hopf algebras whose coradical is the group algebra of a central extension of an abelian group. They fall into families associated to a semisimple Lie algebra together with a Dynkin diagram automorphism. We show conversely that every finite‐dimensional pointed Hopf algebra over a nonabelian group with nonsimple ...
Iván Angiono +2 more
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Differential graded Koszul duality: An introductory survey
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1551-1640, August 2023., 2023 Abstract This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir L. Positselski, Memoirs of the American Math. Society 212 (2011), no. 996, vi+133. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between DG‐algebras and curved DG‐coalgebras, as ...
Leonid Positselski
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On the connection between Hopf–Galois structures and skew braces
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1726-1748, August 2023., 2023 Abstract We present a different version of the well‐known connection between Hopf–Galois structures and skew braces, building on a recent paper of A. Koch and P. J. Truman. We show that the known results that involve this connection easily carry over to this new perspective, and that new ones naturally appear. As an application, we present new insights
Lorenzo Stefanello, Senne Trappeniers
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Semisimple four‐dimensional topological field theories cannot detect exotic smooth structure
Journal of Topology, Volume 16, Issue 2, Page 542-566, June 2023., 2023 Abstract We prove that semisimple four‐dimensional oriented topological field theories lead to stable diffeomorphism invariants and can therefore not distinguish homeomorphic closed oriented smooth four‐manifolds and homotopy equivalent simply connected closed oriented smooth four‐manifolds.
David Reutter
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Hecke algebras and the Schlichting completion for discrete quantum groups
Journal of the London Mathematical Society, Volume 107, Issue 3, Page 843-885, March 2023., 2023 Abstract We introduce Hecke algebras associated to discrete quantum groups with commensurated quantum subgroups. We study their modular properties and the associated Hecke operators. In order to investigate their analytic properties we adapt the construction of the Schlichting completion to the quantum setting, thus obtaining locally compact quantum ...
Adam Skalski +2 more
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Strong z°‐Submodules of a Module
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 Let R be a commutative ring with an identity. The purpose of this paper is to introduce and investigate the notion of strong z°‐submodules of an R‐module as an extension of z°‐submodules and quasi z°‐submodules.
Faranak Farshadifar, Marco Fontana
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Comodules over weak multiplier bialgebras [PDF]
, 2014 This is a sequel paper of arXiv:1306.1466 in which we study the comodules over a regular weak multiplier bialgebra over a field, with a full comultiplication.
Böhm, Gabriella
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[Retracted] Double Weak Hopf Quiver and Its Path Coalgebra
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 The main input of this research is the introduction of the concept of double weak Hopf quiver (DWHQ). In addition, the structures of weak Hopf algebra (WHA) are obtained through path coalgebra of the proposed quivers. Furthermore, the module and comodule structures on the said WHA are discussed.
Muhammad Naseer Khan +6 more
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Weak Hopf Algebra and Its Quiver Representation
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 This study induced a weak Hopf algebra from the path coalgebra of a weak Hopf quiver. Moreover, it gave a quiver representation of the said algebra which gives rise to the various structures of the so‐called weak Hopf algebra through the quiver. Furthermore, it also showed the canonical representation for each weak Hopf quiver.
Muhammad Naseer Khan +5 more
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The Quantum Symmetry in Nonbalanced Hopf Spin Models Determined by a Normal Coideal Subalgebra
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 For a finite‐dimensional cocommutative semisimple Hopf C∗‐algebra H and a normal coideal ∗‐subalgebra H1, we define the nonbalanced quantum double D(H1; H) as the crossed product of H with H1op∧, with respect to the left coadjoint representation of the first algebra acting on the second one, and then construct the infinite crossed product AH1=⋯⋊H⋊H1∧⋊H⋊
Xin Qiaoling, Cao Tianqing, Naihuan Jing
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