Results 11 to 20 of about 3,096 (57)
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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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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[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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Twin TQFTs and Frobenius Algebras
Journal of Mathematics, Volume 2013, Issue 1, 2013., 2013 We introduce the category of singular 2‐dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of generators and relations.
Carmen Caprau, Roberto A. Kraenkel
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Algebraic Structures Based on a Classifying Space of a Compact Lie Group
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We analyze the algebraic structures based on a classifying space of a compact Lie group. We construct the connected graded free Lie algebra structure by considering the rationally nontrivial indecomposable and decomposable generators of homotopy groups and the cohomology cup products, and we show that the homomorphic image of homology generators can be
Dae-Woong Lee, Teoman Özer
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Quantum Groupoids Acting on Semiprime Algebras
Advances in Mathematical Physics, Volume 2011, Issue 1, 2011., 2011 Following Linchenko and Montgomery′s arguments we show that the smash product of an involutive weak Hopf algebra and a semiprime module algebra, satisfying a polynomial identity, is semiprime.
Inês Borges +2 more
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The Khovanov‐Lauda 2‐Category and Categorifications of a Level Two Quantum SL(N) Representation
International Journal of Mathematics and Mathematical Sciences, Volume 2010, Issue 1, 2010., 2010 We construct 2‐functors from a 2‐category categorifying quantum sl(n) to 2‐categories categorifying the irreducible representation of highest weight 2ωk.
David Hill, Joshua Sussan, Aaron Lauda
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Remarks on some infinitesimal symmetries of Khovanov–Rozansky homologies in finite characteristic
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3597-3613, November 2025.Abstract We give a new proof of a theorem due to Shumakovitch and Wang on base point independence of Khovanov–Rozansky homology in characteristic p$p$. Some further symmetries of gl(p)$\mathfrak {gl}(p)$‐homology in characteristic p$p$ are also discussed.
You Qi +3 more
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